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IMA Newsletter #389

March 2009

2008-2009 Program

Mathematics and Chemistry

See http://www.ima.umn.edu/2008-2009 for a full description of the 2008-2009 program on Mathematics and Chemistry.

News and Notes

IMA Events

IMA Tutorial

Introduction to Control, Coherence, and Dissipative Dynamics

March 1, 2009

Speakers: Jean-Michel Coron (Université de Paris VI (Pierre et Marie Curie)), Herschel A. Rabitz (Princeton University), Gabriel Turinici (Université de Paris IX (Paris-Dauphine))

IMA Annual Program Year Workshop

Coherence, Control, and Dissipation

March 2-6, 2009

Organizers: Karl Kunisch (Karl-Franzens-Universität Graz), Claude Le Bris (CERMICS), David A. Micha (University of Florida), David J. Tannor (Weizmann Institute of Science), Gabriel Turinici (Université de Paris IX (Paris-Dauphine))

Public Lecture

Sports Scheduling and the Practice of Operations Research

March 4, 2009

Speakers: Michael Trick (Carnegie-Mellon University)

IMA Workshop

Higher Order Geometric Evolution Equations: Theory and Applications from Microfluidics to Image Understanding

March 23-26, 2009

Organizers: Andrea L. Bertozzi (University of California), Ron Fedkiw (Stanford University), Anette (Peko) Hosoi (Massachusetts Institute of Technology), Stanley J. Osher (University of California), Guillermo R. Sapiro (University of Minnesota Twin Cities)
Schedule

Sunday, March 1

8:15am-8:45amCoffee and registrationEE/CS 3-176 T3.1.09
8:45am-9:00amWelcome to the IMAFadil Santosa (University of Minnesota)EE/CS 3-180 T3.1.09
9:00am-11:00amTutorial on control theory Jean-Michel Coron (Université de Paris VI (Pierre et Marie Curie))EE/CS 3-180 T3.1.09
11:00am-11:30amCoffeeEE/CS 3-176 T3.1.09
11:30am-12:30pmMathematical modelization and numerical approaches in quantum control Gabriel Turinici (Université de Paris IX (Paris-Dauphine))EE/CS 3-180 T3.1.09
12:30pm-2:00pmLunch T3.1.09
2:00pm-3:30pmControlling events at the atomic and molecular scales through Hamiltonian manipulation Herschel A. Rabitz (Princeton University)EE/CS 3-180 T3.1.09
3:30pm-4:00pmCoffee and discussionsEE/CS 3-180 T3.1.09

Monday, March 2

All Day Morning Session: Dissipation I
Afternoon Session: Control I
W3.2-6.09
8:15am-8:45amRegistration and coffeeEE/CS 3-176 W3.2-6.09
8:45am-9:00amWelcome to the IMAFadil Santosa (University of Minnesota)EE/CS 3-180 W3.2-6.09
9:00am-9:30amNon-Markovian quantum dynamics: Foundations and applications to relaxation and transport processesHeinz-Peter Breuer (Albert-Ludwigs-Universität Freiburg)EE/CS 3-180 W3.2-6.09
9:30am-9:50amDiscussionEE/CS 3-180 W3.2-6.09
9:50am-10:20amSingular perturbations and Lindblad-Kossakowski differential equations Pierre Rouchon (École Nationale Supérieure des Mines de Paris)EE/CS 3-180 W3.2-6.09
10:20am-10:40amDiscussionEE/CS 3-180 W3.2-6.09
10:40am-11:10amCoffee breakEE/CS 3-176 W3.2-6.09
11:10am-11:40amOptimal control of laser cooling: A theory of purity increasing transformationsDavid J. Tannor (Weizmann Institute of Science)EE/CS 3-180 W3.2-6.09
11:40am-12:00pmDiscussionEE/CS 3-180 W3.2-6.09
12:00pm-12:30pmPanel discussionDavid J. Tannor (Weizmann Institute of Science)EE/CS 3-180 W3.2-6.09
12:30pm-2:00pmLunch W3.2-6.09
2:00pm-2:30pmControlling events at the atomic and molecular scales through Hamiltonian manipulationHerschel A. Rabitz (Princeton University)EE/CS 3-180 W3.2-6.09
2:30pm-2:50pmDiscussion EE/CS 3-180 W3.2-6.09
2:50pm-3:20pmControllability for a coupled system of Schrödinger equations modeling a trapped ionJean-Pierre Puel (Université Versailles/Saint Quentin-en-Yvelines)EE/CS 3-180 W3.2-6.09
3:20pm-3:40pmDiscussionEE/CS 3-180 W3.2-6.09
3:40pm-4:10pmCoffee breakEE/CS 3-176 W3.2-6.09
4:10pm-4:40pmPanel discussionGabriel Turinici (Université de Paris IX (Paris-Dauphine))EE/CS 3-180 W3.2-6.09

Tuesday, March 3

All DayMorning Session: Control and Dissipation I
Afternoon Session: Control and Dissipation II
W3.2-6.09
8:15am-8:45amCoffeeEE/CS 3-176 W3.2-6.09
8:45am-9:15amWeak field control employing the stochastic surrogate HamiltonianRonnie Kosloff (Hebrew University)EE/CS 3-180 W3.2-6.09
9:15am-9:35amDiscussionEE/CS 3-180 W3.2-6.09
9:35am-10:05amOn a parametrization of the symplectic group with applications to quantum controlViswanath Ramakrishna (University of Texas at Dallas)EE/CS 3-180 W3.2-6.09
10:05am-10:25amDiscussionEE/CS 3-180 W3.2-6.09
10:25am-10:55amCoffee breakEE/CS 3-176 W3.2-6.09
10:55am-11:25amPreserving and extending quantum coherence: from the spin echo effect to fault tolerant quantum computationDaniel Lidar (University of Southern California)EE/CS 3-180 W3.2-6.09
11:25am-11:45amDiscussionEE/CS 3-180 W3.2-6.09
11:45am-12:15pmPanel discussion David A. Micha (University of Florida)EE/CS 3-180 W3.2-6.09
12:15pm-2:00pmLunch W3.2-6.09
2:00pm-2:30pmEnvironmental decoherence in quantum-classical systemsRaymond Kapral (University of Toronto)EE/CS 3-180 W3.2-6.09
2:30pm-2:50pmDiscussionEE/CS 3-180 W3.2-6.09
2:50pm-3:00pmGroup Photo W3.2-6.09
3:00pm-3:30pmCoffee breakEE/CS 3-176 W3.2-6.09
3:30pm-4:00pmFeedback and time optimal control for quantum spin systemsKazufumi Ito (North Carolina State University)EE/CS 3-180 W3.2-6.09
4:00pm-4:20pmDiscussionEE/CS 3-180 W3.2-6.09
4:20pm-4:50pmPanel discussionEnrique Zuazua (Basque Center for Applied Mathematics)EE/CS 3-180 W3.2-6.09
5:00pm-6:30pmReception and Poster Session
Poster submissions welcome from all participants
Lind Hall 400 W3.2-6.09
Laser-induced currents along molecular wire junctions: control in the presence of decoherence due to vibronic couplingsIgnacio Franco (Northwestern University)
Lyapunov control of Schrödinger equations: beyond the dipole approximationAndreea Grigoriu (Université de Paris IX (Paris-Dauphine))
Catalin Lefter (University "Al. I. Cuza" of Iaşi)
Landscape of unitary Transformation in controlled quantum dynamicsTak-San Ho (Princeton University)
Density matrix treatment of optical response with combined instantaneous and delayed dissipations: Adsorbates on solid surfaces David A. Micha (University of Florida)
Explicit, implicit and parametric invariant manifolds for model reduction in chemical kinetics Vladimir A. Sobolev (Samara State University)
Canards, black swans and control of chemical reactionsVladimir A. Sobolev (Samara State University)
Universal families and quantum control in infinite dimensionsRui Vilela Mendes (Instituto Superior Tecnico)
Quantum dissipation and quantum transport: Exact theory and efficient implementationYiJing Yan (Hong Kong University of Science and Technology)
Xiao Zheng (Hong Kong University of Science and Technology)
Fast and accurate computational techniques for the optimal control of quantum systemsGregory John von Winckel (Karl-Franzens-Universität Graz)

Wednesday, March 4

All Day Morning Session: Coherence I
Afternoon Session: Coherence II
W3.2-6.09
8:10am-8:30amCoffeeEE/CS 3-176 W3.2-6.09
8:30am-9:00amElectronically non-adiabatic dynamics via semiclassical initial value methodsWilliam H. Miller (University of California, Berkeley)EE/CS 3-180 W3.2-6.09
9:00am-9:20amDiscussionEE/CS 3-180 W3.2-6.09
9:20am-9:50amA greedy algorithm for the identification of quantum systemsYvon Maday (Université de Paris VI (Pierre et Marie Curie))EE/CS 3-180 W3.2-6.09
9:50am-10:10amDiscussionEE/CS 3-180 W3.2-6.09
10:10am-10:40amCoffee breakEE/CS 3-176 W3.2-6.09
10:40am-11:10amManipulating quantum pathways of matter by coherent nonlinear spectroscopy with classical fields and entangled photonsShaul Mukamel (University of California, Irvine)EE/CS 3-180 W3.2-6.09
11:10am-11:30amDiscussionEE/CS 3-180 W3.2-6.09
11:30am-12:00pmHamiltonian and Markovian reservoir engineering for quantum systemsSonia Schirmer (University of Cambridge)EE/CS 3-180 W3.2-6.09
12:00pm-12:20pmDiscussionEE/CS 3-180 W3.2-6.09
12:20pm-12:50pmPanel discussionDavid F. Coker (Boston University)EE/CS 3-180 W3.2-6.09
12:50pm-2:30pmLunch W3.2-6.09
2:30pm-3:00pmQuantum photochemistry: Incorporation of decoherence in semiclassical treatments of electronically nonadiabatic molecular dynamicsDonald G. Truhlar (University of Minnesota)EE/CS 3-180 W3.2-6.09
3:00pm-3:20pmDiscussion EE/CS 3-180 W3.2-6.09
3:20pm-3:50pmWaves, numerics, control, dispersion and dissipationEnrique Zuazua (Basque Center for Applied Mathematics)EE/CS 3-180 W3.2-6.09
3:50pm-4:10pmDiscussionEE/CS 3-180 W3.2-6.09
4:10pm-4:40pmPanel discussionKarl Kunisch (Karl-Franzens-Universität Graz)EE/CS 3-180 W3.2-6.09
6:00pm-7:00pmMath Matters Public Lecture ReceptionWilley Hall Atrium W3.2-6.09
7:00pm-8:15pmMatters Lecture: Sports Scheduling and the Practice of Operations ResearchMichael Trick (Carnegie Mellon University)Willey Hall 125 W3.2-6.09

Thursday, March 5

All Day Morning Session: Control and Dissipation III
Afternoon Session: Coherence and Dissipation
W3.2-6.09
8:10am-8:30amCoffeeEE/CS 3-176 W3.2-6.09
8:30am-9:00amMonotonically convergent algorithms for solving quantum optimal control problems in chemistry and physicsYukiyoshi Ohtsuki (Tohoku University)EE/CS 3-180 W3.2-6.09
9:00am-9:20amDiscussionEE/CS 3-180 W3.2-6.09
9:20am-9:50amControllability and nonlinearity: Applications to Schrödinger control systemsJean-Michel Coron (Université de Paris VI (Pierre et Marie Curie))EE/CS 3-180 W3.2-6.09
9:50am-10:10amDiscussionEE/CS 3-180 W3.2-6.09
10:10am-10:40amCoffee breakEE/CS 3-176 W3.2-6.09
10:40am-11:10amQuantum dissipation theory: From solvation dynamics to quantum transportYiJing Yan (Hong Kong University of Science and Technology)EE/CS 3-180 W3.2-6.09
11:10am-11:30amDiscussionEE/CS 3-180 W3.2-6.09
11:30am-12:00pmDissipative dynamics in quantum and nonholonomic systemsAnthony Michael Bloch (University of Michigan)EE/CS 3-180 W3.2-6.09
12:00pm-12:20pmDiscussionEE/CS 3-180 W3.2-6.09
12:20pm-12:50pmPanel discussionYvon Maday (Université de Paris VI (Pierre et Marie Curie))EE/CS 3-180 W3.2-6.09
12:50pm-2:30pmLunch W3.2-6.09
2:30pm-3:00pmNonadiabatic solvation dynamics and decoherence: a molecular hydrodynamic approachIrene Burghardt (École Normale Supérieure)EE/CS 3-180 W3.2-6.09
3:00pm-3:20pmDiscussionEE/CS 3-180 W3.2-6.09
3:20pm-3:50pmCoffee breakEE/CS 3-176 W3.2-6.09
3:50pm-4:20pmLimits on control of spin dynamics in the presence of decoherenceNavin Khaneja (Harvard University)EE/CS 3-180 W3.2-6.09
4:20pm-4:40pmDiscussionEE/CS 3-180 W3.2-6.09
4:40pm-5:10pmPanel discussionOleg Prezhdo (University of Washington)EE/CS 3-180 W3.2-6.09
6:30pm-8:30pmWorkshop dinnerPagoda Restaurant
1417 4th St. SE
Minneapolis, MN
612-378-4710
W3.2-6.09

Friday, March 6

All DayControl II W3.2-6.09
8:15am-8:45amCoffeeEE/CS 3-176 W3.2-6.09
8:45am-9:15amQuantum internal model principle and decoherence controlTzyh-Jong Tarn (Washington University)EE/CS 3-180 W3.2-6.09
9:15am-9:35amDiscussionEE/CS 3-180 W3.2-6.09
9:35am-10:05amFeedback schemes for radiation damping suppression in NMR: a control-theoretical perspective Claudio Altafini (International School for Advanced Studies (SISSA/ISAS))EE/CS 3-180 W3.2-6.09
10:05am-10:25amDiscussionEE/CS 3-180 W3.2-6.09
10:25am-10:55amCoffee breakEE/CS 3-176 W3.2-6.09
10:55am-11:25amMaxwell-Schrödinger equations for ultrashort intense laser pulse propagation in molecular mediaAndré D. Bandrauk (University of Sherbrooke)EE/CS 3-180 W3.2-6.09
11:25am-11:45amDiscussionEE/CS 3-180 W3.2-6.09

Monday, March 9

10:45am-11:15amCoffee breakLind Hall 400

Tuesday, March 10

10:45am-11:15amCoffee breakLind Hall 400
11:15am-12:15pmThe ground state energy of heavy atoms: Relativistic lowering of the leading energy correctionHeinz Siedentop (Ludwig-Maximilians-Universität München)Lind Hall 305 PS

Wednesday, March 11

10:45am-11:15amCoffee breakLind Hall 400

Thursday, March 12

10:45am-11:15amCoffee breakLind Hall 400
1:00pm-2:00pmReading group for Professor Ridgway Scott's book "Digital Biology"L. Ridgway Scott (University of Chicago)Lind Hall 401

Friday, March 13

10:45am-11:15amCoffee breakLind Hall 400

Monday, March 16

10:45am-11:15amCoffee breakLind Hall 400

Tuesday, March 17

10:45am-11:15amCoffee breakLind Hall 400
11:15am-12:25pmA model for liver homeostasis using a modified mean-reverting Ornstein-Uhlenbeck processWei Xiong (University of Minnesota)Lind Hall 305 PS
2:00pm-3:00pmReading group for Professor Ridgway Scott's book "Digital Biology"L. Ridgway Scott (University of Chicago)Lind Hall 401

Wednesday, March 18

10:45am-11:15amCoffee breakLind Hall 400

Thursday, March 19

10:45am-11:15amCoffee breakLind Hall 400

Friday, March 20

All DayUniversity of Minnesota Floating Holiday. The IMA is closed.

Monday, March 23

8:15am-9:00amRegistration and coffee EE/CS 3-176 SW3.23-26.09
9:00am-9:15amWelcome to the IMAFadil Santosa (University of Minnesota)EE/CS 3-180 SW3.23-26.09
9:15am-10:00amNatural gradient flow discretization of viscous thin films on curved geometriesMartin Rumpf (Rheinische Friedrich-Wilhelms-Universität Bonn)EE/CS 3-180 SW3.23-26.09
10:00am-10:45amA spectral method with window technique for the initial value problems of the Kadomtsev-Petviashvili equationChiu Yen Kao (University of Minnesota)EE/CS 3-180 SW3.23-26.09
10:45am-11:15amBreakEE/CS 3-176 SW3.23-26.09
11:15am-12:00pmCoarsening: transient and self-similar dynamics in 1-DThomas Peter Witelski (Duke University)EE/CS 3-180 SW3.23-26.09
12:00pm-2:00pmLunch SW3.23-26.09
2:00pm-2:45pmDiffuse interface model of interface problems with curvature dependent energies Qiang Du (Pennsylvania State University)EE/CS 3-180 SW3.23-26.09
2:45pm-3:30pmViscous fingering-like instability of cell fragments: a non-linear analysisMartine Ben Amar (École Normale Supérieure)EE/CS 3-180 SW3.23-26.09
3:30pm-3:40pmGroup photo SW3.23-26.09
4:00pm-5:30pmReception and Poster Session
Poster submissions welcome from all participants
Instructions
Lind Hall 400 SW3.23-26.09
Step evolution for crystals of finite size: The ADL caseHala Al Hajj Shehadeh (New York University)
Asymptotic dynamics of attractive-repulsive swarms Andrew Joel Bernoff (Harvey Mudd College)
Chad Michael Topaz (Macalester College)
Tear film dynamics on an eye-shaped domain: Pressure boundary conditionsRichard J. Braun (University of Delaware)
A multigrid method for the dual formulation of total variation-based image restorationJamylle Laurice Carter (San Francisco State University)
Numerical study of the parameters α and β in the Navier–Stokes-αβ equations for turbulenceEliot Fried (McGill University)
A gradient flow approach to a free boundary droplet model Natalie Grunewald (Rheinische Friedrich-Wilhelms-Universität Bonn)
Statistical models of criminal behavior: The effects of law enforcement actionsPaul Ashton Jones (University of California, Los Angeles)
On instabilities of finite-size films and rivuletsLou Kondic (New Jersey Institute of Technology)
Phase-field model of self-assembled copolymer monolayerHsiang-Wei Lu (Harvey Mudd College)
Dewetting of thin liquid filmsAndreas Münch (University of Nottingham)
Thin fluid films with surfactantEllen Peterson (North Carolina State University)
Michael Shearer (North Carolina State University)
Local existence of solutions to a PDE model of criminal behaviorNancy Rodriguez (University of California, Los Angeles)
Shape optimizer neededAndreas Savin (Université de Paris VI (Pierre et Marie Curie))
Microfluidics enhanced novel materials synthesisAmy Shen (University of Washington)
On the planar extensional motion of an inertially-driven liquid sheet Linda B. Smolka (Bucknell University)
Effect of boundary conditions on mixing efficiencyJames Springham (University of Leeds)
Rob Sturman (University of Leeds)
Eulerian indicators for predicting mixing efficiencyRob Sturman (University of Leeds)
Instabilities and Taylor dispersion in isothermal binary thin fluid filmsBurt S. Tilley (Franklin W. Olin College of Engineering)
The viscous N-vortex problem: A generalized Helmholtz-Kirchhoff approachDavid Thomas Uminsky (Boston University)
High order geometric and potential driving PDEs for image and surface analysisGuowei Wei (Michigan State University)
Memory as vibration in a disconnecting air bubble Wendy W. Zhang (University of Chicago)
Head-on impact of liquid dropsWendy W. Zhang (University of Chicago)

Tuesday, March 24

8:30am-9:00amCoffeeEE/CS 3-176 SW3.23-26.09
9:00am-9:45amBodies and boundaries interacting with complex fluidsMichael J. Shelley (New York University)EE/CS 3-180 SW3.23-26.09
9:45am-10:30amGeneralized Newton-type methods for energy formulations in image processingLeah Bar (University of Minnesota)EE/CS 3-180 SW3.23-26.09
10:30am-11:00amBreakEE/CS 3-176 SW3.23-26.09
11:00am-11:45amDroplet microfluidics experiments: Challenges for modeling and controlRobin L. Garrell (University of California, Los Angeles)EE/CS 3-180 SW3.23-26.09
11:45am-1:30pmLunch SW3.23-26.09
1:30pm-2:15pmA comparison of lumped and field models for electrowetting of sessile dropsAli Nadim (Claremont Graduate University)EE/CS 3-180 SW3.23-26.09
2:15pm-3:00pmEffects of Riemannian curvature on the analysis of landmark shape manifoldsMario Micheli (University of California, Los Angeles)EE/CS 3-180 SW3.23-26.09
3:00pm-3:30pmBreakEE/CS 3-176 SW3.23-26.09
3:30pm-4:15pmComplex variable methods and moving boundary problems Linda J. Cummings (New Jersey Institute of Technology)EE/CS 3-180 SW3.23-26.09
4:15pm-4:45pmDiscussionEE/CS 3-180 SW3.23-26.09

Wednesday, March 25

8:30am-9:00amCoffeeEE/CS 3-176 SW3.23-26.09
9:00am-9:45amPrecursors to splashing on a solid surfaceMichael P. Brenner (Harvard University)EE/CS 3-180 SW3.23-26.09
9:45am-10:30amOn countercurrent two-layer flows in thin channelsBurt S. Tilley (Franklin W. Olin College of Engineering)EE/CS 3-180 SW3.23-26.09
10:30am-11:00amBreakEE/CS 3-176 SW3.23-26.09
11:00am-11:45amDynamics of thin liquid filmsRachel Levy (Harvey Mudd College)EE/CS 3-180 SW3.23-26.09
11:45am-1:30pmLunch SW3.23-26.09
1:30pm-2:15pmGeometrical evolution problems at low Reynolds numbers: reduced modelsDarren G. Crowdy (Imperial College London)EE/CS 3-180 SW3.23-26.09
2:15pm-3:00pmA second-order method for Poisson's equation with discontinuous coefficients and singular sourcesJoseph M. Teran (University of California, Los Angeles)EE/CS 3-180 SW3.23-26.09
3:00pm-3:30pmBreakEE/CS 3-176 SW3.23-26.09
3:30pm-4:15pmA Cahn-Hilliard functional with long-range interactions: (i) steady states and the phase diagram, (ii) small volume fraction asymptotics and gradient flow dynamicsRustum Choksi (Simon Fraser University)EE/CS 3-180 SW3.23-26.09
4:15pm-4:45pmDiscussionEE/CS 3-180 SW3.23-26.09
6:30pm-8:30pmWorkshop dinnerCaspian Bistro
2418 University Ave SE
Minneapolis, MN 55414
612-623-1133
SW3.23-26.09

Thursday, March 26

8:30am-9:00amCoffeeEE/CS 3-176 SW3.23-26.09
9:00am-9:45amSobolev active contours as alternatives to higher-order flowsAnthony J. Yezzi (Georgia Institute of Technology)EE/CS 3-180 SW3.23-26.09
9:45am-10:30amSelf-similar rupture of thin films with strong slipBarbara Niethammer (University of Oxford)EE/CS 3-180 SW3.23-26.09
10:30am-11:00amBreakEE/CS 3-176 SW3.23-26.09
11:00am-11:45amBregmanized methods for sparse reconstruction and restorationStanley J. Osher (University of California, Los Angeles)EE/CS 3-180 SW3.23-26.09
11:45am-12:00pmClosing remarksEE/CS 3-180 SW3.23-26.09

Friday, March 27

All DayIllinois/Missouri Applied Harmonic Analysis Seminar University of Illinois, Urbana-Champaign
10:45am-11:15amCoffee breakLind Hall 400

Monday, March 30

10:45am-11:15amCoffee breakLind Hall 400

Tuesday, March 31

10:45am-11:15amCoffee breakLind Hall 400

Event Legend:

PSIMA Postdoc Seminar
SW3.23-26.09Higher Order Geometric Evolution Equations: Theory and Applications from Microfluidics to Image Understanding
T3.1.09Introduction to Control, Coherence, and Dissipative Dynamics
W3.2-6.09Coherence, Control, and Dissipation
Abstracts
Illinois/Missouri Applied Harmonic Analysis Seminar
Abstract: Information on the meeting (including speakers, and travel funding for participants) is at University of Illinois, Urbana-Champaign. Note the Seminar will be followed by the AMS Central Section meeting, March 27-29, at the University of Illinois.
Discussion
Abstract: No Abstract
Hala Al Hajj Shehadeh (New York University) Step evolution for crystals of finite size: The ADL case
Abstract: We study the step evolution of crystal structures relaxing toward flat surface when the number of steps is finite. We assume that the mass transport process on the structure's surface is attachment-detachment limited (ADL). We propose a fourth order PDE for the slope of the profile as a function of its height. This PDE is derived from the step equations of motion. The solution is asymptotically self-similar. We prove existence and uniqueness of the self-similar solution in the discrete setting.
Claudio Altafini (International School for Advanced Studies (SISSA/ISAS)) Feedback schemes for radiation damping suppression in NMR: a control-theoretical perspective
Abstract: In NMR spectroscopy, the collective measurement is weakly invasive and its back-action is called radiation damping. The aim of this talk is to provide a control-theoretical analysis of the problem of suppressing this radiation damping. It is shown that the two feedback schemes commonly used in the NMR practice correspond one to a high gain oputput feedback for the simple case of maintaining the spin 1/2 in its inverted state, and the second to a 2-degree of freedom control design with a prefeedback that exactly cancels the radiation damping field. A general high gain feedback stabilization design not requiring the knowledge of the radiation damping time constant is also investigated.
André D. Bandrauk (University of Sherbrooke) Maxwell-Schrödinger equations for ultrashort intense laser pulse propagation in molecular media
Abstract: Interaction of ultrashort intense laser pulses with molecular media leads to highly nonlinear nonperturbative effects which can only be treated by large scale computation on massively parallel computers. Single molecule response to such pulses leads to Molecular High Order Harmonic Generation, MHOHG, (1), from which one can synthesize new "attosecond" pulses necessary to control electron dynamics at the natural time scale of the electron, the attoseocond (10**-18 s), (2).The single molecular response can be obtained from high level quantum Time-Dependent Schrödinger,TDSE, simulations. The collective macroscopic response of a molecular medium requires solving many TDSE,s (>10**5)coupled to the classical laser (photon) Maxwell equations (3). We will present the numerical methods necessary to achieve this goal, especially the problem of transparent and artificial boundary condition techniques in view of the different time scales, photon vs electron. Results will be shown for attosecond pulse generation and pulse filamentation in an aligned molecular medium, the one electron H2+ system(4).

(1).A D Bandrauk et al,"Molecular Harmonic Generation," in Progress in Ultrafast Intense Laser Science, vol III, edit K. Yamanouchi (Springer V, NY,2008), chapt 9.
(2).A D Bandrauk,F Krausz, A Starace, "Focus on Attosecond Physics," New J Phys, 10, 025004(2008).
(3).E Lorin,S Chelkowski, A D Bandrauk,"Maxwell-Schrödinger Equations for Nonlinear Laser Propagation in Molecular Media," Comput. Phys. Commun. 177, 908 (2007).
(4).E Lorin,S Chelkowski,A D bandrauk,"Attosecond Pulse Generation for Aligned Molecules," New J Phys, 10, 025033(2008).

Leah Bar (University of Minnesota) Generalized Newton-type methods for energy formulations in image processing
Abstract: Many problems in image processing are addressed via the minimization of a cost functional. The most prominently used optimization technique is gradient-descent, often used due to its simplicity and applicability where other techniques, e.g., those coming from discrete optimization, can not be applied. Yet, gradient-descent suffers from slow convergence, and often to just local minima which highly depend on the initialization and the condition number of the functional Hessian. Newton-type methods, on the other hand, are known to have a faster, quadratic, convergence. In its classical form, the Newton method relies on the L2-type norm to define the descent direction. In this work, we generalize and reformulate this very important optimization method by introducing Newton-type methods based on more general norms. Such norms are introduced both in the descent computation (Newton step), and in the corresponding stabilizing trust-region. This generalization opens up new possibilities in the extraction of the Newton step, including benefits such as mathematical stability and the incorporation of smoothness constraints. We first present the derivation of the modified Newton step in the calculus of variation framework needed for image processing. Then, we demonstrate the method with two common objective functionals: variational image deblurring and geometric active contours for image segmentation. We show that in addition to the fast convergence, norms adapted to the problem at hand yield different and superior results.
Martine Ben Amar (École Normale Supérieure) Viscous fingering-like instability of cell fragments: a non-linear analysis
Abstract: I will present an hydrodynamic model for the motility of keratocytes or fibroblasts on substrates in vitro. Cells or fragment of cells have been observed to switch from a stationary round state to a motile and anisotropic crescent-shaped state. Experimentally, a polarization of the actin network occurs in a preferred direction prior to motility and determins the direction of motion. In this talk, I will present first the model for actin flow of Callan-Jones et al for two-dimensionnal cells lying on a substrate with a strong friction. Using Schwarz function techniques, we derive a dynamic equation for the shape contour including the polymerisation-depolymerisation process and show that static circular shapes are stable for enough tension of the lipidic membrane. We extend the model to incorporate the actin cortex whose anisotropy is due to a preferred orientation at the lipidic membrane. To do so, we use the theory of active polar gels of Kruse et al. inspired from the theory of liquid crystals. Since this cortex has a size of order one ten of the cell, we perform a boundary layer analysis. The presence of the cortex is responsible for a modification of the boundary conditions at the cell border. We show that an increase of the motor activity destabilisizes the cell in the tensile case but we also show that a polarization of the whole actin network is necessary to induce a translation motion.
Andrew Joel Bernoff (Harvey Mudd College), Chad Michael Topaz (Macalester College) Asymptotic dynamics of attractive-repulsive swarms
Abstract: We classify and predict the asymptotic dynamics of a class of swarming models. The model consists of a conservation equation in one dimension describing the movement of a population density field. The velocity is found by convolving the density with a kernel describing attractive-repulsive social interactions. The kernel's first moment and its limiting behavior at the origin determine whether the population asymptotically spreads, contracts, or reaches steady-state. For the spreading case, the dynamics approach those of the porous medium equation. The widening, compactly-supported population has edges that behave like traveling waves whose speed, density and slope we calculate. For the contracting case, the dynamics of the cumulative density approach those of Burgers' equation. We derive an analytical upper bound for the finite blow-up time after which the solution forms one or more δ-functions.
Anthony Michael Bloch (University of Michigan) Dissipative dynamics in quantum and nonholonomic systems
Abstract: In this talk we study the dissipative dynamics arising from coupling to an infinite field in both the classical and quantum context. In particular we study dissipative dynamics generalizing the classical Lamb model. We apply this to the study of dissipation arising in certain controlled quantum systems and also study a model which allows us to quantize certain nonholonomic systems. In the latter case we consider nonholonomic constraints as arising from the limit of a frictional force and then implement the force by an external field which we then quantize. Other methods of quantizing nonholonomic systems will also be discussed.
Richard J. Braun (University of Delaware) Tear film dynamics on an eye-shaped domain: Pressure boundary conditions
Abstract: We model the evolution of human tear film during relaxation (after a blink) using lubrication theory and explore the effects of viscosity, surface tension, gravity and boundary conditions that specify the pressure. The governing nonlinear partial differential equation is solved on an overset grid by a method of lines using finite differences in space and an adaptive second order backward difference formula solver in time. Our two-dimensional simulations, calculated in the Overture framework, display sensitivity in the flow around the boundary to both our choice between two different pressure boundary conditions and to the presence of gravity. The simulations recover features seen in one-dimensional simulations and capture some experimental observations including hydraulic connectivity around the lid margins.
Michael P. Brenner (Harvard University) Precursors to splashing on a solid surface
Abstract: A high velocity impact between a liquid droplet and a solid surface produces a splash. Classical work traced the origin of the splash to a thin sheet of liquid ejected near the impact point. Mechanisms of sheet formation have heretofore relied on initial contact of the droplet and the surface. We demonstrate that, neglecting intermolecular forces between the liquid and the solid, the liquid does not contact the solid, and instead spreads on a very thin air film. The interface of the droplet develops a high curvature and emits capillary waves.
Heinz-Peter Breuer (Albert-Ludwigs-Universität Freiburg) Non-Markovian quantum dynamics: Foundations and applications to relaxation and transport processes
Abstract: Realistic quantum mechanical systems are influenced through the coupling to an environment containing a large number of mostly uncontrollable degrees of freedom. This unavoidable interaction of an open quantum systems with its environment leads to the mechanisms of dissipation and damping, and to a strong and often rapid loss of quantum coherence. The talk begins with a brief introduction into the standard theory of quantum mechanical relaxation which is based on the Markov approximation and on the concepts of completely positive dynamical semigroups and of quantum master equations in Lindblad form. Many examples for this approach are known from quantum optics, decoherence theory, quantum Brownian motion and quantum measurement and control theory. However, strong couplings or interactions with low-temperature reservoirs generally lead to large system-environment correlations which result in long memory times and in a failure of the Markov approximation. To describe the basic features of the non-Markovian quantum dynamics of open systems we develop several new methods as, for example, the technique of correlated projection superoperators [1] and the concept of quantum semi-Markov processes [2]. A number of examples and applications to structured and finite reservoirs [3], to electron spin dynamics in quantum dots [4], and to the problem of quantum transport in nano-structures [5] will be discussed. [1] H. P. Breuer, Phys. Rev. A 75, 022103 (2007). [2] H. P. Breuer and B. Vacchini, Phys. Rev. Lett. 101, 140402 (2008). [3] H. P. Breuer, J. Gemmer and M. Michel, Phys. Rev. E73, 016139 (2006). [4] E. Ferraro, H. P. Breuer, A. Napoli, M. A. Jivulescu, and A. Messina, Phys. Rev. B78, 064309 (2008). [5] R. Steinigeweg, H. P. Breuer and J. Gemmer, Phys. Rev. Lett. 99, 150601 (2007).
Irene Burghardt (École Normale Supérieure) Nonadiabatic solvation dynamics and decoherence: a molecular hydrodynamic approach
Abstract: We present a recently developed mixed quantum-classical method which accounts for the evolution of a quantum subsystem coupled to a non-equilibrium environment (solvent) described in an extended hydrodynamic setting [1]. Starting from a hybrid quantum-classical phase-space distribution, coupled equations for the quantum-classical local density and momentum density are derived which feature the characteristic population-coherence coupling of the nonadiabatic quantum evolution. A generalized free energy functional is introduced, which is similar to the functionals used in dynamical density functional theory (DDFT) methods [2] but is adapted to the quantum-classical setting. The relevant functionals involve two-particle (or, more generally, n-particle) correlation functions that are constructed from state-specific microscopic solute-solvent interactions. A microscopic Marcus-type functional for polar solvation is considered as a special case. The present formulation is particularly appropriate to describe ultrafast solvation dynamics coupled with charge transfer, for example in photochemical charge transfer processes. By the explicit consideration of quantum coherence, the details of population transfer and its susceptibility to decoherence effects, become amenable to direct investigation. First numerical examples are presented [3] and the extension of the formalism beyond the free energy functional formulation are addressed, in particular in view of including non-equilibrium solvent correlations. [1] I. Burghardt and B. Bagchi, Chem. Phys. 329, 343 (2006). [2] B. Bagchi and A. Chandra, Adv. Chem. Phys. LXXX, 1 (1991); U. Marini Bettolo Marconi and P. Tarazona, J. Chem. Phys. 110, 8032 (1999); A. J. Archer and R. Evans, J. Chem. Phys. 121, 4246 (2004). [3] P. Ramanathan, S. Parry, S.-L. Zhao, K. H. Hughes, and I. Burghardt, to be submitted.
Jamylle Laurice Carter (San Francisco State University) A multigrid method for the dual formulation of total variation-based image restoration
Abstract: We present a multigrid method for solving the dual formulation of the Total Variation-based problem in image restoration. Flat regions of the desired image contribute to the slow convergence of the widely-used Chambolle method. Numerical results confirm that the multigrid method with a modified Chambolle smoother is many orders of magnitude faster than the original Chambolle method.
Rustum Choksi (Simon Fraser University) A Cahn-Hilliard functional with long-range interactions: (i) steady states and the phase diagram, (ii) small volume fraction asymptotics and gradient flow dynamics
Abstract: We consider a Cahn-Hilliard functional with long-range interactions. This functional was introduced as a qualitative way of modeling self-assembly of diblock copolymers. We will consider the phase diagram from the point of view of numerical simulations. We will also describe analytical work, via Gamma convergence, on the asymptotics of the energy in the small volume fraction limit. Our results will be compared with a formal study on the H-1 gradient-flow of the functional, demonstrating separate regimes for coarsening and self-assembly (pattern formation). This talk will encompass recent work with M. Peletier (Eindhoven), J.F. Williams (SFU), M. Maras (SFU), and with K. Glasner (Arizona).
David F. Coker (Boston University) Panel discussion
Abstract: No Abstract
Jean-Michel Coron (Université de Paris VI (Pierre et Marie Curie)) Tutorial on control theory
Abstract: The aim of this tutorial is to present basic results (e.g., on controllability, observability, feedback laws...) in control theory of systems modeled by ordinary differential equations. First, we give the classical results for linear control systems. Then, we give the direct applications of this linear theory to local results for nonlinear control systems. Finally, we present some more advanced tools to deal with global properties and with the case where the linearized control system is not controllable. We illustrate the methods presented on simple physical systems.
Jean-Michel Coron (Université de Paris VI (Pierre et Marie Curie)) Controllability and nonlinearity: Applications to Schrödinger control systems
Abstract: In this talk we survey some methods to study the controllability of nonlinear control systems modeled by partial differential equations, namely:
1. The return method,
2. Power series expansions,
3. Quasi-static deformations.
These methods will be illustrated on quantum systems.
Darren G. Crowdy (Imperial College London) Geometrical evolution problems at low Reynolds numbers: reduced models
Abstract: In this talk we report on some mathematical techniques for modelling evolving geometries at low Reynolds numbers. Two problems will be discussed, both involving free capillary surfaces. The first is a study of organisms swimming in Stokes flows in the presence of free surfaces. An idealized mathematical model is presented whereby the swimmer's interaction with a free capillary surface is captured. The second problem is of industrial importance involving the optimal design of thin optic fibres with microstructure. There is much interest in reducing transmission loss in optic fibres by careful design of the microstucture imparted to a fibre during the ``drawing process'' in which molten glass is pulled through a casting die. During this process, geometrical changes in the microstucture take place owing to capillary effects resulting in the need to understand a highly nonlinear inverse problem. New ideas for modelling this process will be described.
Linda J. Cummings (New Jersey Institute of Technology) Complex variable methods and moving boundary problems
Abstract: We will selectively review the application of complex variable methods to moving boundary problems, with specific reference to the Hele-Shaw problem, and slow viscous flow driven by surface tension (in 2D, or quasi-2D). Established theory and results will be discussed, as well as some open questions and new directions.
Qiang Du (Pennsylvania State University) Diffuse interface model of interface problems with curvature dependent energies
Abstract: In this talk, we report some recent works on the diffuse interface models of some interface problems with curvature dependent interfacial energies such as the Helfrich elastic bending energy for vesicle membranes. We discuss various theoretical and computational issues related to the diffuse interface approach and present some simulation results for the deformation of vesicle membranes in a number of environmental conditions.
Ignacio Franco (Northwestern University) Laser-induced currents along molecular wire junctions: control in the presence of decoherence due to vibronic couplings
Abstract: The effect of electron-vibrational interactions on the electronic transport induced by femtosecond omega + 2omega laser fields along unbiased molecular nanojunctions is investigated. For this, the photoinduced vibronic dynamics of trans-polyacetylene oligomers coupled to macroscopic metallic leads is followed in a mean-field mixed quantum- classical approximation. A reduced description of the dynamics is obtained by introducing projective lead-molecule couplings and deriving an effective Schrödinger equation satisfied by the orbitals in the molecular region. Two possible rectification mechanisms are identified and investigated. The first one relies on near-resonance photon absorption and is shown to be fragile to the ultrafast electronic decoherence processes introduced by the wire's vibrations. The second one employs the dynamic Stark effect and is demonstrated to be highly efficient and robust to electron-vibrational interactions.
Eliot Fried (McGill University) Numerical study of the parameters α and β in the Navier–Stokes-αβ equations for turbulence
Abstract: We perform numerical studies of the Navier–Stokes-αβ equations, which are based on a general framework for fluid-dynamical theories with gradient dependencies. Specifically, we examine the effect of the length scales α and β on the energy spectrum in three-dimensional statistically homogeneous and isotropic turbulent flows in a periodic cubic domain, including the limiting cases of the Navier–Stokes-α and Navier–Stokes equations. A significant increase in the accuracy arises for β < α, but an optimal choice of these scales depends on the grid resolution.
Robin L. Garrell (University of California, Los Angeles) Droplet microfluidics experiments: Challenges for modeling and control
Abstract: Microfluidic devices without walls have many advantages over channel-based devices. In droplet-based (“digital”) microfluidics, liquids are transported as droplets between parallel plates, rather than as streams. The droplets are created, moved, joined and divided by applying electrical potentials sequentially between electrodes buried beneath a hydrophobic dielectric layer. The resulting device is completely reconfigurable. Samples can be processed in series or simultaneously, each in the same way or through a unique sequence of steps. We have found shown that droplets of a wide range of liquids can be actuated by electrowetting, dielectrophoresis, or a combination of the two. An electromechanical model has been developed that explains the relative ease with which different liquids can be actuated and provides the basis for designing devices and operating conditions for actuating particular liquids. Applications of droplet microfluidics include separations by precipitation, solid phase extraction and liquid-liquid phase transfer. Understanding and controlling these processes represent significant new challenges to the modeling community.
Andreea Grigoriu (Université de Paris IX (Paris-Dauphine)), Catalin Lefter (University "Al. I. Cuza" of Iaşi) Lyapunov control of Schrödinger equations: beyond the dipole approximation
Abstract: In this joint work with Gabriel Turinici, we analyse the Lyapunov trajectory tracking of the Schrödinger equation for a second order coupling operator. We present a theoretical convergence result; for situations not covered by the first theorem we propose a numerical approach and complement it with a second theoretical result.
Natalie Grunewald (Rheinische Friedrich-Wilhelms-Universität Bonn) A gradient flow approach to a free boundary droplet model
Abstract: We consider a quasi–stationary free boundary droplet model. This model does not satisfy a comparison principle and can have non unique solutions. Nevertheless it can be seen as a gradient flow on the space of possible supports of the drop. The gradient flow formulation leads to a natural time discretization, which we employ to show the existence of a weak form of viscosity solutions for the model.
Tak-San Ho (Princeton University) Landscape of unitary Transformation in controlled quantum dynamics
Abstract: The control problem of generating unitary transformations is especially relevant to current research in quantum information processing and computing. Control dynamical landscapes for unitary transformations is analyzed in the infinite dimensional function space of the time-dependent external field. The dynamical analysis reveals many essential geometric features of optimal control landscapes for unitary transformations, including bounds on the local landscape slope and curvature. Close examination of the curvatures at the critical points shows that the unitary transformation control landscapes are free of local traps and proper choices of the adaptation matrix may facilitate the search for optimal control fields producing desired unitary transformations, in particular, in the neighborhood of the global extrema.
Kazufumi Ito (North Carolina State University) Feedback and time optimal control for quantum spin systems
Abstract: A feedback control law is developed for the stochastic control problems for quantum spin systems. It is similar to the one we analyzed for the Schroedinger control system. Also, the time optimal control problem is discussed for the deterministic quantum spin system. An algorithm based on the semismooth Newton method is developed and analyzed. Numerical findings are reported for the spin half system.
Paul Ashton Jones (University of California, Los Angeles) Statistical models of criminal behavior: The effects of law enforcement actions
Abstract: We continue the study, initiated in Short et al., of criminal activities as described by an agent based model with dynamical target affinities. Here we incorporate effect of law enforcement agents on the spatial distribution and overall level of crime in simulated urban settings. Our focus is on a two–dimensional lattice model of residential burglaries, where each site (target) is characterized by a dynamic attractiveness to burglary and where criminal and law enforcement agents are represented by random walkers. The dynamics of the criminal agents and the attractiveness field are, with certain modifications to be detailed, as described in Short et al. Here the dynamics of enforcement agents are affected by the attractiveness field via a biasing of the walk the detailed rules of which define a deployment strategy. We observe that law enforcement agents, if properly deployed, will in fact reduce the total amount of crime, but their relative effectiveness depends on their numbers, the deployment strategy used, and spatial distribution of criminal activity.
Chiu Yen Kao (University of Minnesota) A spectral method with window technique for the initial value problems of the Kadomtsev-Petviashvili equation
Abstract: The Kadomtsev-Petviashvili (KP) equation is a two-dimensional dispersive wave equation which was proposed to study the stability of one soliton solution of the KdV equation under the influence of weak transversal perturbations. It is well know that some closed-form solutions can be obtained by  function which have a Wronskian determinant form. It is of interest to study KP with an arbitrary initial condition and see whether the solution converges to any closed-form solution asymptotically. To reveal the answer to this question both numerically and theoretically, we consider different types of initial conditions, including one-line soliton, V-shape wave and cross-shape wave, and investigate the behavior of solutions asymptotically. We provides a detail description of classification on the results. The challenge of numerical approach comes from the unbounded domain and unvanished solutions in the infinity. In order to do numerical computation on the finite domain, boundary conditions need to be imposed carefully. Due to the non-periodic boundary conditions, the standard spectral method with Fourier methods involving trigonometric polynomials cannot be used. We proposed a new spectral method with a window technique which will make the boundary condition periodic and allow the usage of the classical approach. We demonstrate the robustness and efficiency of our methods through numerous simulations.
Raymond Kapral (University of Toronto) Environmental decoherence in quantum-classical systems
Abstract: Quantum systems that can be usefully partitioned into a subsystem interacting with a bath will be considered. For such systems, a quantum-classical Liouville description of the dynamics is assumed, while retaining the full quantum equilibrium structure of the system. The equations of motion may be cast in the form of a non-Markovian equation for the diagonal elements of the subsystem density matrix. The memory kernel in this equation accounts for all coherences in the system. The conditions under which the memory kernel decays rapidly as a result of averages over quantum or classical bath equilibrium structure will discussed. When such decay is rapid, it will be shown how a lift back to the full phase space results in a Markovian master equation of motion. This equation leads to a surface-hopping trajectory description of the dynamics where each fictitious trajectory accounts for decoherence due to the bath degrees of freedom. The results will be illustrated by simulations of nonadiabatic chemical dynamics. R. Grunwald and R. Kapral, J. Chem. Phys., 126, 114109 (2007).
R. Grunwald, H. Kim and R. Kapral, J. Chem. Phys., 128, 164110 (2008).
Navin Khaneja (Harvard University) Limits on control of spin dynamics in the presence of decoherence
Abstract: An important problem in coherent spectroscopy and quantum information science is to find limits on how close an open quantum dynamical system can be driven to a target state in the presence of dissipation and decoherence. What is the optimal excitation that achieves this objective? We describe these problems in the context of the design of multidimensional NMR experiments that maximize the efficiency of transfer of coherence between coupled spins in the presence of decoherence with the goal of optimizing the sensitivity of these experiments. We present some new mathematical techniques for computing limits on how much coherence or polarization can be transferred between coupled spins in multiple spin topologies.
Lou Kondic (New Jersey Institute of Technology) On instabilities of finite-size films and rivulets
Abstract: Joint work with J. Diez, A. Gonzalez, and R. Rack. We discuss the influence of finite size effects on the breakup process involving finite-size films and rivulets. For films, we show that the breakup process due to finite size effects can be related to the so-called nucleation mode of instability of infinite films. We also consider coupling of different modes of instabilities, and the competition between them. Next, we revisit the classical problem of rivulet instability and discuss whether finite size effects may be important in determining relevant breakup mechanisms. We apply our results to rupture of nano-scale metal lines irradiated by repeated laser pulses and discuss relevance of the considered process to self-assembly on nanoscale.
Ronnie Kosloff (Hebrew University) Weak field control employing the stochastic surrogate Hamiltonian
Abstract: Joint work with Gil Katz, David Gelman, Mark Ratner and Ronnie Kosloff. Simulation of many body quantum dynamics scales exponentially bad with the number of degrees of freedom. Many methods are devoted to obtain a restricted many body wavefunction which still are able to approximate the quantum dynamics. In the context of system bath dynamics the surrogate Hamiltonian method the dynamics is simplified by replacing the bath Hamiltonian by a simpler version which describes the bath faithfully up to a specified time. The computation task becomes even more formidable when the dynamics takes place at a finite temperature, then formally the wavefunction has to be replaced with a density operator. We present a stochastic methods which allows to describe finite temperature dynamics within a wavefunction description. The stochastic methods are applied for the initial thermal sampling. In addition the dynamical description of the bath is extended stochasticly to take care of dephasing and energy relaxation at long times. We use this method to simulate an outstanding problem in coherent control: can we obtain weak field control of a branching ratio? The model consists of a ground state and two excited state potentials. The target is to control the population in these states using phase modulation only.
Karl Kunisch (Karl-Franzens-Universität Graz) Panel discussion
Abstract: No Abstract
Rachel Levy (Harvey Mudd College) Dynamics of thin liquid films
Abstract: Thin liquid films are important in applications involving lubrication or coating, which arise in both biological and industrial contexts. Recent experiments have uncovered new phenomena that present challenges of modeling, analysis and simulation. These include new wave forms, fingering instabilities, and a variety of driving and control mechanisms. Mathematically the class of problems is interesting because surface tension dominates inertia, leading to fourth order nonlinear parabolic partial differential equations. This talk will include recent developments and open problems in theoretical, experimental and applied aspects of thin liquid films.
Daniel Lidar (University of Southern California) Preserving and extending quantum coherence: from the spin echo effect to fault tolerant quantum computation
Abstract: Dynamical decoupling pulse sequences have been used to extend coherence times in quantum systems ever since the discovery of the spin-echo effect. But while for good reasons the nuclear magnetic resonance (NMR) community has typically been content with moderate line narrowing, in quantum computing extremely high levels of coherence are required in order to perform meaningful computational tasks. In this talk I will describe a method of recursively concatenated dynamical decoupling pulses, designed to overcome both decoherence and operational errors [1]. For bounded-strength, non-Markovian environments, such as for the spin-bath that arises in electron- and nuclear-spin based solid-state quantum computer proposals, it is strictly advantageous to use concatenated, as opposed to standard periodic dynamical decoupling pulse sequences. Namely, the concatenated scheme is both fault-tolerant and super-polynomially more efficient, at equal cost [2,3]. Preliminary experimental results on NMR of 13C in adamantene (due to Dieter Suter, Dortmund), and NMR of the 31P donor in Si (due to Steve Lyon, Princeton), demonstrating the advantages of concatenated decoupling, will also be presented. Time permitting, I will describe our recent results on the construction of a universal set of quantum logic gates whose fidelity can be kept arbitrarily high for essentially arbitrarily long times in the presence of coupling to a spin bath, by use of concatenated decoupling. References: [1] K. Khodjasteh and D.A. Lidar, "Fault-Tolerant Quantum Dynamical Decoupling," Phys. Rev. Lett. 95, 180501 (2005). [2] K. Khodjasteh and D.A. Lidar, "Performance of Deterministic Dynamical Decoupling Schemes: Concatenated and Periodic Pulse Sequences," Phys. Rev. A 75, 062310 (2007). [3] K. Khodjasteh and D.A. Lidar, "Rigorous Bounds on the Performance of a Hybrid Dynamical Decoupling-Quantum Computing Scheme," Phys. Rev. A 78, 012355 (2008).
Hsiang-Wei Lu (Harvey Mudd College) Phase-field model of self-assembled copolymer monolayer
Abstract: We develop a phase field model that incorporates the polymer vitrification and diffusion in the self-assembly of polymer blends. Simulation shows the different polymers in the blend cooperate to self-assemble into nanoscale features with varying dimension. The feature dimensions can be tuned by adjusting the blend composition and the surface concentration.
Yvon Maday (Université de Paris VI (Pierre et Marie Curie)) A greedy algorithm for the identification of quantum systems
Abstract: Joint work with Julien Salomon. In this presentation we present and illustrate a greedy algorithm that enables in a first stage to design a set of selective laser fields that can in a second stage be used to identify some unknown parameters of quantum systems for a problem of Hamiltonian Identification.
Yvon Maday (Université de Paris VI (Pierre et Marie Curie)) Panel discussion
Abstract: No Abstract
David A. Micha (University of Florida) Density matrix treatment of optical response with combined instantaneous and delayed dissipations: Adsorbates on solid surfaces
Abstract: Joint work with Andrew S. Leathers (Quantum Theory Project, Departments of Chemistry and of Physics, University of Florida, Gainesville, Florida 32611, U.S.A.). The interaction of light with a localized (primary) region in a many atom system undergoing electronic and vibrational transitions leads to energy dissipation and uctuations through both nearly instantaneous and delayed processes. A fast dissipation typically occurs due to electronic energy relaxation in the medium, while a delayed dissipation arises from vibrational energy relaxation. A theoretical and computational treatment of these phenomena has been done in terms of a reduced density matrix (RDM) satisfying a generalized Liouville-von Neumann equation.[1] Instantaneous dissipation is described by a Lindblad term containing electronic transition rates,[2] while the delayed dissipation is given by a time integral derived from the time-correlation function (TCF) of atomic displacements in the medium.[3] We consider cases where the TCF decays exponentially (fast) or as an inverse power (slowly). An initial thermal equilibrium can not be assumed when there are long lasting interactions between the primary region and the medium. We describe a general procedure that provides the optical response in this case by calculating the difference between solutions for the RDM with and without excitation by a light pulse. We present examples for slow relaxation of optical excitation in CO/Cu(001) and Ag3/Si(111).[4] 1. D. A. Micha, A. Leathers, and B. Thorndyke in "Quantum Dynamics of Complex Molecular Systems" (Springer-Verlag, 2006) D. A. Micha and I. Burghardt, eds., pp. 165-194. 2. D. A. Micha and A. Santana, J. Phys. Chem. A 2003, 107, 7311. 3. A. S. Leathers and D. A. Micha, J. Phys. Chem. A 2006, 110, 749. 4. A. S. Leather, D. A. Micha, and D. S. Kilin, "Density matrix treatment for an electronically excited adsorbate on a solid surface", to be published. Work partly supported by the NSF of the USA, and by the Dreyfus Foundation.
Mario Micheli (University of California, Los Angeles) Effects of Riemannian curvature on the analysis of landmark shape manifolds
Abstract: Shape spaces can be endowed with the structure of Riemannian manifolds; this allows one to compute, for example, Euler-Lagrange equations and geodesic distance for such spaces. Until very recently little was known about the actual geometry of shape manifolds; in this talk we summarize results contained in my recent doctoral dissertation, which deals with the computation of curvature for "Landmarks Shape Spaces." Implications on both the qualitative dynamics of geodesics and the statistical analysis on shape manifolds are also discussed.
William H. Miller (University of California, Berkeley) Electronically non-adiabatic dynamics via semiclassical initial value methods
Abstract: In the late 1970’s Meyer and Miller (MM) [J. Chem. Phys. 70, 3214 (1979)] presented a classical Hamiltonian corresponding to a finite set of electronic states of a molecular system (i.e., the various potential energy surfaces and their couplings), so that classical trajectory simulations could be carried out treating the nuclear and electronic degrees of freedom (DOF) in an equivalent dynamical framework (i.e., by classical mechanics), thereby describing non-adiabatic dynamics in a more unified manner. Much later Stock and Thoss (ST) [Phys. Rev. Lett. 78, 578 (1997)] showed that the MM model is actually not a ‘model’, but rather a ‘representation’ of the nuclear-electronic system; i.e., were the MMST nuclear-electronic Hamiltonian taken as a Hamiltonian operator and used in the Schrödinger equation, the exact (quantum) nuclear-electronic dynamics would be obtained. In recent years various initial value representations (IVRs) of semiclassical (SC) theory have been used with the MMST Hamiltonian to describe electronically non-adiabatic processes. Of special interest is the fact that though the classical trajectories generated by the MMST Hamiltonian (and which are the ‘input’ for an SC-IVR treatment) are 'Ehrenfest trajectories', when they are used within the SC-IVR framework the nuclear motion emerges from regions of non-adiabaticity on one potential energy surface (PES) or another, and not on an average PES as in the traditional Ehrenfest model. Examples are presented to illustrate and (hopefully) illuminate this behavior.
Shaul Mukamel (University of California, Irvine) Manipulating quantum pathways of matter by coherent nonlinear spectroscopy with classical fields and entangled photons
Abstract: Joint work with Oleksiy Roslyakk (Chemistry department, University of California Irvine, USA). Nonlinear optical spectroscopy is commonly formulated semi-classically, i.e. letting a quantum material interact with classical fields. The key quantity in this approach is the nonlinear polarization, characterizing the microscopic response of the material to the incoming fields. Its calculation can be based on either the density matrix or the wave function. The former involves forward propagation in real time and is represented by double sided Feynman diagrams in Liouville space, whereas the latter requires forward and backward propagation in Hilbert space which is carried out on the Schwinger-Keldysh closed time path loop (CTPL). Such loops are extensively used in quantum field theory of non-equilibrium states, but double-sided Feynman diagrams have become a practical tool for the design and analysis of time-domain nonlinear optical experiments. Several fundamental ambiguities which arise in the semi-classical formulation regarding the intuitive interpretation of optical signals are resolved by combining the CTPL with a quantum description of the laser fields. In nonlinear spectroscopy of single molecules, for example, the signal cannot be given in terms of a classical response functions as predicted by the semi-classical theory. Heterodyne detection can be viewed as a stimulated process and does not require a classical local oscillator. The quantum nature of the field requires the introduction of superoperator nonequilibrium Green’s functions (SNGF), which represent both response and spontaneous fluctuations of the material. This formalism allows the computation of nonlinear optical processes involving any combination of classical and quantum optical modes. Closed correlation-function expressions are derived for the combined effects of causal response and non-causal spontaneous fluctuations. Coherent three wave mixing (sum frequency generation (SFG) and parametric down conversion (PDC)) involving one and two quantum optical modes respectively, are connected to their incoherent counterparts: two-photon-induced fluorescence (TPIF) and two-photon-emitted fluorescence (TPEF). We show how two-photon absorption and homodyne detected difference frequency generation conducted with entangled photons can be used to manipulate interference effects and select desired Liouville space pathways of matter. Recently several groups have applied entangled photon pairs in nonlinear spectroscopy (near resonance homodyne detected sum-frequency generation (SFG), two photon induced fluorescence (TPIF) and two-photon absorption (TPA). It was demonstrated that the normally quadratic scaling of the signal with the intensity of the incoming field becomes linear when using entangled photons. This indicates that the two photons effectively act as a single particle, interacting with matter within a narrow time window. This opens new ways for manipulating nonlinear optical signals and revealing new matter information otherwise erased by interference.
  • Processes involving an arbitrary number of classical and quantum modes of the radiation field are treated within the same framework.
  • Loop diagrams can be used to describe all incoherent and coherent (cooperative) signals.
  • A unified approach is provided for both resonant and off-resonant measurements. In the latter the material enters as a parameter in an effective Hamiltonian for the field.
  • Nonlinear spectroscopy conducted with resonant classical fields only accesses the causal response function. Quantum fields reveal the broader SNGF's family which carry additional information about fluctuations.
  • Spectroscopy with quantum entangled fields may be described.
  1. "Nonlinear Spectroscopy with Entangled Photons Manipulating Quantum Pathways of Matter," O. Rosyak, C. Marx and S. Mukamel, Phys. Rev. A. (In press, 2009).
  2. "Photon Entanglement Signatures in Homodyne Detected Difference Frequency Gene," O. Roslyak and S. Mukamel, Optics Express 17, 1093 (2009).
  3. "Nonlinear Optical Spectroscopy of Single, Few and Many Molecules; Nonequilibrium Green’s Function QED Approach," C.A. Marx, U. Harbola and S. Mukamel, Phys. Rev. A. 77, 022110, 2008.
  4. "A Unified Description of Sum Frequency Generation, Parametric Down Conversion and Two Photon Fluoresence," O. Roslyak, C. Marx and S. Mukamel, Molecular Physics. (In press, 2009).
Andreas Münch (University of Nottingham) Dewetting of thin liquid films
Abstract: We present results on various aspects of thin film models for dewetting films involving high order equations and systems of equations. These include results on the rim instability and the shape of the rim where the liquid dewets, as well as the occurence of non-classical shocks for fast dewetting where inertia becomes important.
Ali Nadim (Claremont Graduate University) A comparison of lumped and field models for electrowetting of sessile drops
Abstract: After a brief overview of electrohydrodynamics including Maxwell's electric stress tensor under AC fields where the medium has both conductive and dielectric characteristics, we focus on the problem of electrowetting actuation of sessile drops on a patterned array of electrodes with a thin dielectric coating. For both the case when the drop is electrically grounded from below and when it is floating, we compute the electric field in the vicinity of the drop over a range of frequencies and use the traction derived from the Maxwell stress tensor to calculate the effective electrowetting force on the drop. At low frequencies where the drop behaves like a perfect conductor, the results are compared with previously derived lumped parameter models for the electrowetting force. [Joint work with James Sterling and Maged Ismail.]
Barbara Niethammer (University of Oxford) Self-similar rupture of thin films with strong slip
Abstract: (Joint work with D. Peschka and A. Muench). We consider a simple model for line rupture of thin fluid films in which Trouton viscosity and van-der-Waals forces balance. For this model there exists a one-parameter family of second kind self-similar solutions. We establish necessary and sufficient conditions for convergence to any self-similar solution in a certain parameter regime. We also present a conjecture on the domains of attraction of all self-similar solutions which is supported by numerical simulations.
Yukiyoshi Ohtsuki (Tohoku University) Monotonically convergent algorithms for solving quantum optimal control problems in chemistry and physics
Abstract: We develop monotonically convergent algorithms for solving typical quantum optimal control problems in chemistry and physics. They include (1) state-to-state control for a system nonlinearly interacting with a control and (2) operator pulse design under the influence of dissipation. We discuss the solution algorithms in a unified manner. As an application of the first algorithm, we consider the alignment/orientation control of diatomic molecules. The alignment is achieved through the polarizability coupling between shaped laser pulses and molecules. When the retaining of the aligned state is chosen as a physical objective, the control pulse is shown to utilize the so-called "coherent destruction of tunneling" mechanisms. This numerical observation is confirmed by using a simple analytical model. Second application is associated with (2). In quantum information processing and quantum computer, the realization of gate operations in physical systems is essential. As the operations should be done with quite high precision, optimal control approaches could be suitable tools for this purpose. We discuss the possibility through case studies such as quantum algorithm simulations and suppression of decoherence.
Stanley J. Osher (University of California, Los Angeles) Bregmanized methods for sparse reconstruction and restoration
Abstract: We started with a project where we denoised normals to surfaces, then fit the surface to the normals, which we regarded as solving a 4th order PDE via some kind of splitting. This led to remarkably successful algorithms for L1 tpe minimizations, constrained and unconstrained. These include L1, TV, B1,1, nonlocal TV,... Bregman iteration, in its various incarnations popped up and turned out to be unreasonably effective. I'll discuss this which is joint work with many people.
Ellen Peterson (North Carolina State University), Michael Shearer (North Carolina State University) Thin fluid films with surfactant
Abstract: Thin liquid films driven by surface tension are considered, both when gravity plays a significant role, as on an inclined plane, and when it is less significant, on a horizontal substrate. Motion of the film is modeled in the lubrication approximation by a fourth order system of PDE. In the case of a horizontal substrate, we examine the influence of insoluble surfactant both experimentally and numerically. In the experiments, we visualize surfactant using fluorescence, and its effect on the thin film using a laser. The numerical code tracks the edge of the surfactant as it propagates. We also analyze the stability of a thin film wave traveling down an inclined plane driven by both surfactant and gravity. Numerical results show the propagation of small disturbances, thereby substantiating the analysis. This is joint work with Karen Daniels, Dave Fallest, Rachel Levy and Tom Witelski.
Oleg Prezhdo (University of Washington) Panel discussion
Abstract: No Abstract
Jean-Pierre Puel (Université Versailles/Saint Quentin-en-Yvelines) Controllability for a coupled system of Schrödinger equations modeling a trapped ion
Abstract: We analyse the possibility of control for a coupled system of Schrödinger equations on the whole real line for the harmonic oscillator modeling a single trapped ion. In fact the coupling is due to the control which acts as a potential and which is performed by three monochromatic waves which can be switched on and off, only one of them being active at each time. By taking the frequency of these waves large enough, we show that this sytem can be approximated by a much simpler one, the so-called Law-Eberly system, for which we can give an explicit control satisfying all requirements. This enables us to prove approximate controllability for the original system in the natural (L2)2 norms and also in much stronger norms. This work has been done in collaboration with Sylvain Ervedoza.
Herschel A. Rabitz (Princeton University) Controlling events at the atomic and molecular scales through Hamiltonian manipulation
Abstract: Since the development of the laser some 40 years ago, a long standing dream has been to utilize this special source of radiation to manipulate dynamical events at the atomic and molecular scales. Hints that this goal may become a reality began to emerge in the 1990's, due to a confluence of concepts and technologies involving (a) control theory, (b) ultrafast laser sources, (c) laser pulse shaping techniques, and (d) fast pattern recognition algorithms. These concepts and tools have resulted in a high speed instrument configuration capable of adaptively changing the driving laser pulse shapes, approaching the performance of thousands of independent experiments in a matter of minutes. Each particular shaped laser pulse acts as a “Photonic Reagent” much as an ordinary reagent would at the molecular scale. Although a Photonic Reagent has a fleeting existence, it can leave a permanent impact. Current demonstrations have ranged from manipulating simple systems (atoms) out to the highly complex (biomolecules), and applications to quantum information sciences are being pursued. In all cases, the fundamental concept is one of adaptively manipulating quantum systems. The principles involved will be discussed, along with the presentation of the state of the field.
Herschel A. Rabitz (Princeton University) Controlling events at the atomic and molecular scales through Hamiltonian manipulation
Abstract: Since the development of the laser some 40 years ago, a long standing dream has been to utilize this special source of radiation to manipulate dynamical events at the atomic and molecular scales. Hints that this goal may become a reality began to emerge in the 1990's, due to a confluence of concepts and technologies involving (a) control theory, (b) ultrafast laser sources, (c) laser pulse shaping techniques, and (d) fast pattern recognition algorithms. These concepts and tools have resulted in a high speed instrument configuration capable of adaptively changing the driving laser pulse shapes, approaching the performance of thousands of independent experiments in a matter of minutes. Each particular shaped laser pulse acts as a "Photonic Reagent" much as an ordinary reagent would at the molecular scale. Although a Photonic Reagent has a fleeting existence, it can leave a permanent impact. Current demonstrations have ranged from manipulating simple systems (atoms) out to the highly complex (biomolecules), and applications to quantum information sciences are being pursued. In all cases, the fundamental concept is one of adaptively manipulating quantum systems. The principles involved will be discussed, along with the presentation of the state of the field.
Viswanath Ramakrishna (University of Texas at Dallas) On a parametrization of the symplectic group with applications to quantum control
Abstract: The talk will report on a parametrization of the real symplectic group in four dimensions. One feature of this parametrization is that it yields the polar decomposition of a symplectic matrix via the solution of simple quadratic equations. Applications to the study of squeezing transformations will be presented. Extensions to higher dimensions will be discussed.
Pierre Rouchon (École Nationale Supérieure des Mines de Paris) Singular perturbations and Lindblad-Kossakowski differential equations
Abstract: In this joint work with Mazyar Mirrahimi, we consider an ensemble of quantum systems described by a density matrix, solution of a Lindblad-Kossakowski differential equation. We focus on the special case where the decoherence is only due to a highly unstable excited state and where the spontaneously emitted photons are measured by a photo-detector. We propose a systematic method to eliminate the fast and asymptotically stable dynamics associated to the excited state in order to obtain another differential equation for the slow part. We show that this slow differential equation is still of Lindblad-Kossakowski type, that the decoherence terms and the measured output depend explicitly on the amplitudes of quasi-resonant applied field, i.e., the control. Beside a rigorous proof of the slow/fast (adiabatic) reduction based on singular perturbation theory, we also provide a physical interpretation of the result in the context of coherence population trapping via dark states and decoherence-free subspaces. Numerical simulations illustrate the accuracy of the proposed approximation for a 5-level systems.
Martin Rumpf (Rheinische Friedrich-Wilhelms-Universität Bonn) Natural gradient flow discretization of viscous thin films on curved geometries
Abstract: The talk will focus on the numerical approximation of the evolution of a thin viscous films on a curved geometry. Here, the concept of natural time discretization for gradient flows is revisited. This is based on an explicit balance between the energy decay and the corresponding dissipation to be invested. In case of thin films the dissipation is formulated in terms of a transport field, whereas the energy primarily depends on the film profile. The velocity field and the film height are coupled by the underlying transport equation. Hence, one is naturally led to a PDE constraint optimization problem and duality techniques from optimization are applied in the minimization algorithm. For the space discretization a discrete exterior calculus approach is investigated. The method can be generalized to the simulate thin coatings.
Andreas Savin (Université de Paris VI (Pierre et Marie Curie)) Shape optimizer needed
Abstract: Motivation:
It is possible to relate the concept of chemical bond to the region of three-dimensional space where the probability to find exactly one pair of electrons is maximal. Characteristics:
- The computation of the probability for a given volume chosen can be time-consuming. It requires the eigenvalues of a matrix having elements computed from integrals over the volume.
- The shape derivatives can vary strongly from one part of the delimiting surface to another.
- Multiple solutions exist by the nature of the problem. However, the user might have a good intuition of what they are and choose a good starting volume.
Sonia Schirmer (University of Cambridge) Hamiltonian and Markovian reservoir engineering for quantum systems
Abstract: Hamiltonian engineering has been shown to be a powerful technique, which can be applied to many different problems that involve steering a quantum system to achieve a desirable outcome, and a particularly promising approach to Hamiltonian engineering is the optimal control approach, i.e., formulating the problem as an optimization problem. However, the problem formulation is important, and although optimization is a well-established field, the solution of the resulting optimization problems is usually not trivial, in part because the search space is usually infinite dimensional. To overcome this obstacle the controls must be parametrized, and the parametrization is critical. The most common approach is to approximate the controls using piecewise constant functions. While adequate for some problems, such a parametrization inevitably leads to high bandwidth solutions due to the discontinuities of the fields. We demonstrate that using more natural parameterizations we can significantly reduce the bandwidth of the fields, although at the expense of having to solve more complex optimization problems. Another crucial variable is the problem formulation itself. Often, optimal control problems are formulated using Hamiltonians that incorporate many approximations, e.g., RWA, off-resonant excitations and fixed couplings negligible, etc, which inevitably limit what can be achieved by optimal control. We show that we can in principle speed up the implementation of quantum gates several orders of magnitude compared to conventional frequency-selective geometric control pulses for certain systems by avoiding such approximations and taking advantage of the full range of off-resonant excitations and couplings available in the optimal control framework. Another problem with Hamiltonian engineering is that the most effective approaches are model-based, i.e., we require a model of the system, especially its response to external fields, or the functional dependence on the controls. In some cases this isn't a problem and optimal controls can be designed to be robust with regard to model uncertainties. For other problems, however, such as information transfer through spin networks using simple local actuators, it can be shown that the optimal switching sequences are highly model-dependent, while the exact network topology and precise couplings for such systems are usually not known. Such problems call for closed loop optimization. We show that we can effectively solve problems such as finding optimal switching time sequences for such networks by adapting gradient-based optimization algorithms even for problems where the standard evolutionary algorithms fail completely to find acceptable solutions. Finally, there are certain types of problems that Hamiltonian engineering, although an extremely powerful tool for quantum engineering, cannot solve. One such problem is stabilization in the presence of environmental interactions. This problem can in principle be addressed using reservoir engineering. We consider a variant of Markovian reservoir engineering using direct feedback from an indirect measurement such as homodyne detection. We show that if the control and feedback Hamiltonians in this setting are unrestricted and we have some degree of control over the type of measurement we can perform, then any state can be in principle be stabilized.
Michael J. Shelley (New York University) Bodies and boundaries interacting with complex fluids
Abstract: Most classical and modern studies of swimming, pumping, and mixing in fluids have considered fluids that are Newtonian. All of these phenomena also take place in fluids that are viscoelastic and at low Reynolds number, and are particularly important to biology and to engineering areas such as microfluidics. I will discuss theoretical studies of the effect of viscoelasticity on low Reynolds number undulatory swimming and peristaltic pumping. I will also discuss an example of how symmetry breaking instabilities in extensional flows of a viscoelastic fluid can lead to new coherent structures and fluid mixing.
Amy Shen (University of Washington) Microfluidics enhanced novel materials synthesis
Abstract: The flow of complex fluids in confined geometries produces rich and new phenomena due to the interaction between the intrinsic length-scales of the fluid and the geometric length-scales of the device. In this poster, we will show three examples to illustrate how self-assembly, confinement, and flow can be used to control fluid microstructure and enhance the controlled synthesis of bio-compatible nanomaterials and supramolecular hydrogels.
Heinz Siedentop (Ludwig-Maximilians-Universität München) The ground state energy of heavy atoms: Relativistic lowering of the leading energy correction
Abstract: Formulae for the ground state energy E(Z) of atoms in the limit of large atomic number Z have been a very active area of research. Among the most prominent contributions in the context of Schrödinger operators are the ground breaking work of Lieb and Simon (1977) and the seminal papers of Fefferman and Seco (1989-1994). However, large Z results for non-relativistic models are questionable from a physical point of view: the innermost electrons of heavy atoms come close to the nucleus where they move very fast. Therefore, a relativistic model is important. We prove that the leading energy correction, the Scott correction – intuitively due to the innermost electrons – is indeed lowered compared with the Schrödinger case. Our proof is valid up to and including the critical coupling constant. It is based on a renormalization of the energy whose zero level we adjust to be the ground-state energy of the corresponding non-relativistic problem. This -- together with a new Gagliaro-Nierenberg inequality – allows us to roll the proof back to results for the Schrödinger operator. The talk is based on joint work with Rupert Frank and Simone Warzel (both Princeton).
Linda B. Smolka (Bucknell University) On the planar extensional motion of an inertially-driven liquid sheet
Abstract: We derive a time-dependent exact solution of the free surface problem for the Navier-Stokes equations that describes the planar extensional motion of a viscous sheet driven by inertia. The linear stability of the exact solution to one- and two-dimensional symmetric perturbations is examined in the inviscid and viscous limits within the framework of the long-wave or slender body approximation. Both transient growth and long-time asymptotic stability are considered. For one-dimensional perturbations in the axial direction, viscous and inviscid sheets are asymptotically marginally stable, though depending on the Reynolds and Weber numbers transient growth can have an important effect. For one-dimensional perturbations in the transverse direction, inviscid sheets are asymptotically unstable to perturbations of all wavelengths. For two-dimensional perturbations, inviscid sheets are unstable to perturbations of all wavelengths with the transient dynamics controlled by axial perturbations and the long-time dynamics controlled by transverse perturbations. The asymptotic stability of viscous sheets to one-dimensional transverse perturbations and to two-dimensional perturbations depends on the capillary number (Ca); in both cases, the sheet is unstable to longwave transverse perturbations for any finite Ca. This work is in collaboration with Thomas P. Witelski.
Vladimir A. Sobolev (Samara State University) Explicit, implicit and parametric invariant manifolds for model reduction in chemical kinetics
Abstract: In this joint work with Elena Shchepakina we use a geometric singular perturbations method for reducing the model order in chemical kinetics problems. The method relies on the theory of integral manifolds, which essentially replaces the original system by another system on an integral manifold with dimension equal to that of the slow subsystem. Explicit, implicit and parametric representations of a slow invariant manifolds are used.
Vladimir A. Sobolev (Samara State University) Canards, black swans and control of chemical reactions
Abstract: In this joint work with Elena Shchepakina we consider a canard trajectory (in the case of scalar slow variable) and a black swan (in the case of vector slow variable) as the result of gluing attractive and repulsive slow integral manifolds, due to the availability of an additional parameter (function in the case of vector slow variable) in the differential system. As a result we obtain the continuous attractive/repulsive slow invariant surface. It is possible to consider the gluing parameter (function) as a special kind of partial feedback control, which guarantees the safety of chemical regimes, even with perturbations, during a chemical process.
James Springham (University of Leeds), Rob Sturman (University of Leeds) Effect of boundary conditions on mixing efficiency
Abstract: We consider the mixing of fluid by chaotic advection. Many well-studied examples may be modeled by a class of dynamical systems known as linked-twist maps. The mathematical discipline of ergodic theory studies concepts such as mixing which will be familiar to experimentalists. New analytical results for linked-twist maps suggest mixing rates similar to those observed experimentally and numerically.
Rob Sturman (University of Leeds) Eulerian indicators for predicting mixing efficiency
Abstract: Mixing is inherently a Lagrangian phenomenon, a property of the movement of fluid particles. Many different methods exist for measuring, quantifying and predicting the quality of a mixing process, all involving evolution of individual trajectories. We propose indicative tools which are formulated using only Eulerian information, and illustrate their use briefly on a variety of different model mixers.
David J. Tannor (Weizmann Institute of Science) Panel discussion
Abstract: No Abstract
David J. Tannor (Weizmann Institute of Science) Optimal control of laser cooling: A theory of purity increasing transformations
Abstract: The powerful techniques of Optimal Control Theory (OCT), used in recent years to design laser pulse sequences to control chemical bond breaking, are applied to the problem of laser cooling in an open system. The result is a striking new mechanism in which spontaneous emission builds coherences between all the populated levels creating a pure state, only at the end of the process transferring the amplitude to the lowest energy state. This novel mechanism accelerates the cooling process by exploiting the cooling induced by spontaneous emission to all the ground electronic state levels, not just the lowest level. The mechanism suggests the calibration of cooling in terms of increasing purity of the system as measured by the quantity Tr(rho2). An analytical theory of the cooling mechanism is developed in terms of a two-stage interplay between the control fields and the spontaneous emission. One of the main results of the analytical theory is a differential equation for the optimal cooling rate. The key components of the theory – the definition of cooling as purity increase; the invariance of purity to control fields; and the maximum rate of approach to absolute zero – correspond to the zeroth, second and third law of thermodynamics, providing a thermodynamic framework for laser cooling. The formulation of cooling in terms of the coherence measure Tr(rho2) has an additional, interesting implication: that our results carry over immediately to the problem of control of quantum decoherence, suggesting both a new mechanism and fundamental limitations on the control of that process.
Tzyh-Jong Tarn (Washington University) Quantum internal model principle and decoherence control
Abstract: Decoherence, which is caused due to the interaction of a quantum system with its environment plagues all quantum systems and leads to the loss of quantum properties that are vital for quantum computation and quantum information processing. In this work we propose a novel strategy using techniques from systems theory to completely eliminate decoherence and also provide conditions under which it can be done so. A novel construction employing an auxiliary system, the bait, which is instrumental to decoupling the system from the environment, is presented. This corresponds to the Internal Model Principle for Quantum Mechanical Systems. Almost all the earlier work on decoherence control employ density matrix and stochastic master equations to analyze the problem. Our approach to decoherence control involves the bilinear input affine model of quantum control system which lends itself to various techniques from classical control theory, but with non-trivial modifications to the quantum regime. The elegance of this approach yields interesting results on open loop decouplability and Decoherence Free Subspaces (DFS). Additionally, the feedback control of decoherence may be related to disturbance decoupling for classical input affine systems, which entails careful application of the methods by avoiding all the quantum mechanical pitfalls. The two concepts are contrasted and an improved theory of disturbance decoupling for general input affine systems is developed. In the process of calculating a suitable feedback the system has to be restructured due to its tensorial nature of interaction with the environment, which is unique to quantum systems. Finally the results are also shown to be superior to the ones obtained via master equations. In order to apply feedback a reliable information extraction scheme using continuous indirect measurements with the help of a quantum probe is outlined. Finally, a methodology to synthesize feedback parameters itself is given, that technology permitting, could be implemented for practical 2-qubit systems to perform decoherence free Quantum Computing.
Joseph M. Teran (University of California, Los Angeles) A second-order method for Poisson's equation with discontinuous coefficients and singular sources
Abstract: Numerical simulation of moving interface problems often requires the solution of elliptic PDEs involving coefficients that can be discontinuous and sources that are singular. Since the interface is moving, it is advantageous to solve the problem on a fixed Eulerian grid which does not conform to the interface as it moves. We propose an intuitive new method which acheives second order accurate results in L-infinity on a fixed cartesian grid with embedded interfaces. The method is largely independent of the geometry and the interface can be represented either as an arbitrary (closed) segmented curve or a levelset. The problem is formulated as a variational constrained minimization problem which preserves a symmetric positive definite discretization.
Burt S. Tilley (Franklin W. Olin College of Engineering) On countercurrent two-layer flows in thin channels
Abstract: Two-phase gas-liquid flows are important in a variety of heat transfer systems, such as in the on-chip cooling of microelectromechanical devices up to the infrastructure of safety systems in nuclear power plants. We focus on the case of two-layer flows in inclined channels, where a gas and a liquid, immiscibly separated by a sharp interface with large surface tension, flow in opposite directions. The liquid is driven by gravity while the gas flows due to an imposed pressure gradient. For disturbance wavelengths that are much longer than the channel thickness, a fourth-order nonlinear equation which describes the evolution of the separating interfacial shape is found that is coupled to an elliptic equation for the pressure, whose solution provides a constraint to the dynamics of the flow. We survey the impact of these different constraints on the solutions, and extend the analysis to include incompressibility effects. This work was a collaboration with T.M. Segin and L. Kondic.
Burt S. Tilley (Franklin W. Olin College of Engineering) Instabilities and Taylor dispersion in isothermal binary thin fluid films
Abstract: Joint work with Z. Borden, H. Grandjean, L. Kondic, and A.E. Hosoi. Experiments with glycerol-water thin films flowing down an inclined plane reveal a localized instability that is primarily three-dimensional. These transient structures, referred to as "dimples", appear initially as nearly isotropic depressions on the interface. A linear stability analysis of a binary mixture model in which barodiffusive effects dominate over thermophoresis (i.e. the Soret effect) reveals unstable modes when the components of the mixture have different bulk densities and surface tensions. This instability occurs when Fickian diffusion and Taylor dispersion effects are small, and is driven by solutalcapillary stresses arising from gradients in concentration of one component, across the depth of the film. Qualitative comparison between the experiments and the linear stability results over a wide range of parameters is presented.
Michael Trick (Carnegie Mellon University) Matters Lecture: Sports Scheduling and the Practice of Operations Research
Abstract: Major League Baseball is a multi-billion dollar per year industry that relies heavily on the quality of its schedule. Teams, fans, TV networks, and even political parties (in a way revealed in the talk) rely on the schedule for profits and enjoyment. Only recently have the computational tools of operations research been powerful enough to address the issue of finding "optimal" schedules. Trick will discuss his experiences in scheduling college basketball, major league baseball, and other sports, and show how operations research is revolutionizing the way sports scheduling is done.
Donald G. Truhlar (University of Minnesota) Quantum photochemistry: Incorporation of decoherence in semiclassical treatments of electronically nonadiabatic molecular dynamics
Abstract: The talk will begin with an introduction to the quantum master equation (Liouville-von Neumann equation), followed by a discussion of how we have used this equation it in a semiclassical algorithm for calculating of non-Born-Oppenheimer molecular dynamics. I will also discuss the physical origin of decoherence in electronically nonadiabatic molecular dynamics and our method for estimating the decoherence time. The resulting treatment will be validated against accurate quantum dynamics for small molecular systems.
Gabriel Turinici (Université de Paris IX (Paris-Dauphine)) Mathematical modelization and numerical approaches in quantum control
Abstract: We address in this talk some practical issues that occur in the design of (optimal) control field that manipulate quantum phenomena. After discussing modelization issues (which functional to optimize, to what goal it corresponds etc) several algorithms will be discussed: genetic/evolutionary algorithm, adjoint state (optimal control) approaches and stabilization (Lyapounov) algorithms.
Gabriel Turinici (Université de Paris IX (Paris-Dauphine)) Panel discussion
Abstract: No Abstract
David Thomas Uminsky (Boston University) The viscous N-vortex problem: A generalized Helmholtz-Kirchhoff approach
Abstract: We give a convergent expansion of solutions of the two-dimensional, incompressible Navier-Stokes equations which generalizes the Helmholtz-Kirchhoff point vortex model to systematically include the effects of both viscosity and finite core size. The evolution of each vortex is represented by a system of coupled ordinary differential equations for the location of its center, and for the coefficients in the expansion of the vortex with respect to a basis of Hermite functions. The differential equations for the evolution of the moments contain only quadratic nonlinearities and we give explicit combinatorial formulas for the coefficients of these terms. We also show that in the limit of vanishing viscosity and core size we recover the classical Helmholtz-Kirchhoff point vortex model.
Rui Vilela Mendes (Instituto Superior Tecnico) Universal families and quantum control in infinite dimensions
Abstract: In a topological space, a family of continuous mappings is called universal if its action, in at least one element of the space, is dense. If the mappings are unitary or trace-preserving completely positive, the notion of universality is closely related to the notion of controllability in either closed or open quantum systems. Quantum controllability in infinite dimensions is discussed in this setting and minimal generators are found for full control universal families. Some of the requirements of the operators needed for control in infinite dimensions follow from the properties of the infinite unitary group. Hence, a brief discussed of this group and their appropriate mathematical spaces is also included.
Guowei Wei (Michigan State University) High order geometric and potential driving PDEs for image and surface analysis
Abstract: A family of high-order geometric and potential driving evolution equations was introduced and applied to image analysis and biomolecular surface formation. Coupled geometric PDEs were introduced for image edge detection.
Thomas Peter Witelski (Duke University) Coarsening: transient and self-similar dynamics in 1-D
Abstract: Motivated by the dewetting of viscous thin films on hydrophobic substrates, we study models for the coarsening dynamics of interacting localized structures in one dimension. For the thin films problem, lubrication theory yields a Cahn-Hilliard-type governing PDE which describes spinodal dewetting and the subsequent formation of arrays of metastable fluid droplets. The evolution for the masses and positions of the droplets can be reduced to a coarsening dynamical system (CDS) consisting of a set of coupled ODEs and deletion rules. Previous studies have established that the number of drops will follow a statistical scaling law, N(t)=O(t-2/5). We derive a Lifshitz-Slyozov-Wagner-type (LSW) continuous model for the drop size distribution and compare it with discrete models derived from the CDS. Large deviations from self-similar LSW dynamics are examined on short- to moderate-times and are shown to conform to bounds given by Kohn and Otto. Insight can be applied to similar models in image processing and other problems in materials science. Joint work with M.B. Gratton (Northwestern Applied Math).
Wei Xiong (University of Minnesota) A model for liver homeostasis using a modified mean-reverting Ornstein-Uhlenbeck process
Abstract: Short of a liver biopsy, hepatic disease and drug-induced liver injury are diagnosed and classified from clinical findings, especially laboratory results. It was hypothesized that a healthy hepatic dynamic equilibrium might be modeled by an Ornstein-Uhlenbeck (OU) stochastic process, which might lead to more sensitive and specific diagnostic criteria. Using pooled data from healthy volunteers in pharmaceutical clinical trials, this model was applied using maximum likelihood methods. It was found that the exponent of the autocorrelation function was proportional to the square root of time rather time itself, as predicted by the OU model. This finding suggests a stronger autocorrelation than expected and may have important implications regarding the use of laboratory testing in clinical diagnosis, in clinical trial design, and in monitoring drug safety.
YiJing Yan (Hong Kong University of Science and Technology) Quantum dissipation theory: From solvation dynamics to quantum transport
Abstract: We have recently developed a hierarchical equations-of-motion (HEOM) approach to nonperturbative and non-Markovian quantum dissipation. It is a unified and exact theory for arbitrary coupling Gaussian environments of distinct nature: bosonic versus fermionic, and canonical versus grand canonical ensembles. It admits also an arbitrary time-dependent external field driving. Two systems will be used to elaborate both the formulation and implementation aspects of the theory. In an electron transfer (ET) system, the bath environment serves as a canonical bosonic ensemble, responsible for the system decoherence and energy relaxation. The validation of Zusman equation will be discussed, on the basis of exact HEOM results. In a quantum transport setup, a molecule or quantum dot is placed in contact with electrodes under applied voltage. Each electrode reservoir serves as a grand canonical fermion ensemble. It is responsible not only for decoherence and energy relaxation, but also for the fermion particle (i.e., electron) transport in/out of the system. The HEOM-based quantum transport theory will be summarized, together with the calculated transient currents through model quantum dot systems and the current spectrums in response to various forms of external time-dependent applied voltage. Support from RGC of Hong Kong Government is acknowledged. R.X. Xu and Y. J. Yan, Phys. Rev. E, 75, 031107 (2007).
J. S. Jin, X. Zheng, and Y. J. Yan, J. Chem. Phys. 128, 234703 (2008).
X. Zheng, J. S. Jin, and Y. J. Yan, J. Chem. Phys. 129, 184112 (2008).
X. Zheng, J. S. Jin, and Y. J. Yan, New J. Phys. 10, 093016 (2008).
YiJing Yan (Hong Kong University of Science and Technology), Xiao Zheng (Hong Kong University of Science and Technology) Quantum dissipation and quantum transport: Exact theory and efficient implementation
Abstract: Joint work with Jinshuang Jin. We present a hierarchical equations-of-motion (HEOM) formalism of quantum dissipation theory [J. Chem. Phys. 128, 234703 (2008)], which is formally exact, practically tractable, and numerically convergent. It characterizes the transient current transport dynamics of arbitrary dissipative many-electron systems, in contact with electrodes under arbitrary temperatures and external fields. The HEOM approach provides a useful theoretical tool to study various transient and stationary properties of many-body systems far away from equilibrium. With an efficient hybrid scheme accounting for the bath correlation functions, we demonstrate accurate transient response current driven by time-dependent applied voltages in both sequential and cotunneling regimes.
Anthony J. Yezzi (Georgia Institute of Technology) Sobolev active contours as alternatives to higher-order flows
Abstract: We discuss the use of "geometric" (i.e. formulated exclusively in terms of a curve's arclength parameter) Sobolev metrics to devise new gradient flows of curves. We refer to the resulting evolving contours as "Sobolev Active Contours". An interesting property of Sobolev gradient flows is that they stabilize many gradient descent processes that are unstable when formulated in the more traditional L2 sense. Furthermore, the order of the gradient flow partial differential equation is reduced when employing the Sobolev metric rather than L2. This greatly facilitates numerical implementation methods since higher order PDE's are replaced by lower order integral-differential PDE's to minimize the exact same geometric energy functional. The fourth order L2 gradient flow for the elastic energy of a curve, for example, is substituted by a second order Sobolev gradient flow for the same energy. In this talk we give some background on Sobolev active contours, show some applications using energy regularizers normally connected with fourth order flows, and present some recent results in visual tracking. Joint work with Ganesh Sundaramoorthi, Andrea Mennucci, Guillermo Sapiro, and Stefano Soatto.
Wendy W. Zhang (University of Chicago) Memory as vibration in a disconnecting air bubble
Abstract: Focusing a finite amount of energy dynamically into a vanishingly small amount of material requires that the initial condition be perfectly symmetric. In reality, imperfections are always present and cut-off the approach towards the focusing singularity. The disconnection of an underwater bubble provides a simple example of this competition between asymmetry and focusing. We use a combination of theory, simulation and experiments to show that the dynamics near disconnection contradicts the prevailing view that the disconnection dynamics converges towards a universal, cylindrically-symmetric singularity. Instead an initial asymmetry in the shape of the bubble neck excites vibrations that persist until disconnection. We argue that such memory-encoding vibrations may arise whenever initial asymmetries perturb the approach towards a singularity whose dynamics has an integrable form.
Wendy W. Zhang (University of Chicago) Head-on impact of liquid drops
Abstract: When two point particles collide, the outcome is governed entirely by energy and momentum conservation, with no dependence on the detailed interaction potential. Here we use a Volume of Fluid (VOF) simulation to examine what happens in the analogous case when two liquid drops collide. At low speeds, the liquid drops rebounce elastically, just as seen for point particles. At high speeds, however, a liquid sheet is ejected along the impact plane. When ambient gas pressure is low, both simple estimates and simulation show that the ejection is dominated by inertial effects. This idea enables us to collapse the pressure variation within the liquid drop at early times. In addition we find that surface tension effects are confined to the rim of the expanding sheet and acts primarily to slow the radial expansion.
Enrique Zuazua (Basque Center for Applied Mathematics) Waves, numerics, control, dispersion and dissipation
Abstract: In this lecture we shall present a survey of recent work on several topics related with numerical approximation of waves. Control Theory is by now and old subject, ubiquitous in many areas of Science and Technology. There is a quite well-established finite-dimensional theory and many progresses have been done also in the context of PDE (Partial Differential Equations). But gluing these two pieces together is often a hard task from a mathematical point of view. This is not a merely mathematical problem since it affects modelling and computational issues. In particular, the following two questions arise: Are finite-dimensional and infinite-dimensional models equally efficient from a control theoretical point of view? Are controls built for finite-dimensional numerical schemes efficient at the continuous level? In this talk we shall briefly analyze these issues for the wave equation as a model example of propagation without damping. We shall show that high frequency spurious oscillations may produce the divergence of the most natural numerical schemes. This confirms the fact that finite and infinite-dimensional modelling may give completely different results from the point of view of control. We shall then discuss some remedies like filtering of high frequencies, multi-grid techniques and numerical viscosity. Similar questions arise when building numerical approximation schemes for nonlinear Schrödinger equations or in other contexts as when designing, for instance, absorving boundary conditions or developping the method of Perfectly Matched Layers (PML) for the wave equation.
Enrique Zuazua (Basque Center for Applied Mathematics) Panel discussion
Abstract: No Abstract
Gregory John von Winckel (Karl-Franzens-Universität Graz) Fast and accurate computational techniques for the optimal control of quantum systems
Abstract: The manipulation and control of quantum systems is fundamental to a host of emerging applications from the design of qubits and novel nanoscale devices, to the control of photochemical reactions as well as atomic and molecular dynamics. Although there are established techniques to simulate the evolution of a quantum system, the problem of finding the control potential which results in a desired evolution is considerably more challenging. Recent contributions to the development of new quantum control methodologies and optimal control formulation are discussed. In particular, the investigation of theoretical issues such as the appropriate choice of function spaces for the control and the non-convex structure of the optimization problems as well as the interplay between discretization and optimization are considered. Accurate and computationally efficient algorithms for computing the optimal controls which take advantage of the underlying physics are introduced with a focus on Krylov-Newton methods for solving controls for fast state transitions in a system.
Visitors in Residence
Jose Vidal Alcala Courant Institute of Mathematical Sciences 3/22/2009 - 3/26/2009
Hala Al Hajj Shehadeh New York University 3/22/2009 - 3/26/2009
Claudio Altafini International School for Advanced Studies (SISSA/ISAS) 2/28/2009 - 3/6/2009
Donald G. Aronson University of Minnesota 9/1/2002 - 8/31/2009
Jorge Balbas California State University 3/22/2009 - 3/26/2009
André D. Bandrauk University of Sherbrooke 3/2/2009 - 3/8/2009
Leah Bar University of Minnesota 3/22/2009 - 3/26/2009
Vincent Joseph Beltrani Princeton University 3/1/2009 - 3/7/2009
Martine Ben Amar École Normale Supérieure 3/22/2009 - 3/26/2009
Andrew Joel Bernoff Harvey Mudd College 3/22/2009 - 3/26/2009
Anthony Michael Bloch University of Michigan 3/3/2009 - 3/6/2009
Richard J. Braun University of Delaware 3/22/2009 - 3/26/2009
Michael P. Brenner Harvard University 3/24/2009 - 3/25/2009
Susanne C. Brenner Louisiana State University 3/22/2009 - 3/26/2009
Heinz-Peter Breuer Albert-Ludwigs-Universität Freiburg 3/1/2009 - 3/8/2009
Peter Brune University of Chicago 9/8/2008 - 6/30/2009
Sun Young Bu University of North Carolina 2/1/2009 - 5/30/2009
Irene Burghardt École Normale Supérieure 3/4/2009 - 3/8/2009
Maria-Carme T. Calderer University of Minnesota 9/1/2008 - 6/30/2009
Hannah Callender University of Minnesota 9/1/2007 - 8/31/2009
Jamylle Laurice Carter San Francisco State University 3/22/2009 - 3/26/2009
Hui-Yu Chen University of Minnesota 3/23/2009 - 3/26/2009
Xianjin Chen University of Minnesota 9/1/2008 - 8/31/2010
Rustum Choksi Simon Fraser University 3/22/2009 - 3/26/2009
David F. Coker Boston University 3/1/2009 - 3/6/2009
Benjamin Cook Areté Associates 3/22/2009 - 3/26/2009
Jean-Michel Coron Université de Paris VI (Pierre et Marie Curie) 2/28/2009 - 3/7/2009
Darren G. Crowdy Imperial College London 3/22/2009 - 3/26/2009
Linda J. Cummings New Jersey Institute of Technology 3/22/2009 - 3/26/2009
Shibin Dai Worcester Polytechnic Institute 3/21/2009 - 3/26/2009
Domenico D'Alessandro Iowa State University 3/1/2009 - 3/3/2009
Daniel Dix University of South Carolina 1/1/2009 - 6/30/2009
Qiang Du Pennsylvania State University 3/22/2009 - 3/26/2009
Julio Duarte Eastman Kodak Company 3/23/2009 - 3/26/2009
Olivier Dubois University of Minnesota 9/3/2007 - 8/31/2009
Robert S. Eisenberg Rush University Medical Center 3/22/2009 - 3/26/2009
James W. Evans Iowa State University 3/15/2009 - 5/22/2009
Gregory Ezra Cornell University 2/18/2009 - 3/7/2009
Ignacio Franco Northwestern University 2/28/2009 - 3/6/2009
Christopher Fraser University of Chicago 8/27/2008 - 6/30/2009
Eliot Fried McGill University 3/22/2009 - 3/26/2009
Wenhua (Bill) Gao University of California, Los Angeles 3/22/2009 - 3/26/2009
Robin L. Garrell University of California, Los Angeles 3/22/2009 - 3/26/2009
Tryphon T. Georgiou University of Minnesota 3/1/2009 - 3/6/2009
Andreea Grigoriu Université de Paris IX (Paris-Dauphine) 2/27/2009 - 3/7/2009
Natalie Grunewald Rheinische Friedrich-Wilhelms-Universität Bonn 3/22/2009 - 3/26/2009
Shiyuan Gu Louisiana State University 3/22/2009 - 3/28/2009
Thirupathi Gudi Louisiana State University 3/22/2009 - 3/27/2009
Xiaoqing He University of Minnesota 3/1/2009 - 3/6/2009
Mark S. Herman University of Minnesota 9/1/2008 - 8/31/2010
Peter Hinow University of Minnesota 9/1/2007 - 8/21/2009
Tak-San Ho Princeton University 3/1/2009 - 3/6/2009
Mary Ann Horn National Science Foundation 3/31/2009 - 3/31/2009
Anette (Peko) Hosoi Massachusetts Institute of Technology 3/22/2009 - 3/26/2009
Jingfang Huang University of North Carolina 12/30/2008 - 5/31/2009
Yanghong Huang University of California, Los Angeles 3/22/2009 - 3/25/2009
Yunkyong Hyon University of Minnesota 9/1/2008 - 8/31/2010
Sharif Ibrahim Washington State University 3/22/2009 - 3/26/2009
Kazufumi Ito North Carolina State University 3/1/2009 - 3/6/2009
Mark Iwen University of Minnesota 9/1/2008 - 8/31/2010
Alexander Izzo Bowling Green State University 9/1/2008 - 6/30/2009
Srividhya Jeyaraman University of Minnesota 9/1/2008 - 8/31/2010
Lijian Jiang University of Minnesota 9/1/2008 - 8/31/2010
Paul Ashton Jones University of California, Los Angeles 3/22/2009 - 3/26/2009
Ning Ju Oklahoma State University 3/22/2009 - 3/27/2009
Chiu Yen Kao University of Minnesota 3/22/2009 - 3/26/2009
Justin C.T. Kao Massachusetts Institute of Technology 3/22/2009 - 3/26/2009
Raymond Kapral University of Toronto 3/2/2009 - 3/5/2009
Markus Keel University of Minnesota 7/21/2008 - 6/30/2009
Navin Khaneja Harvard University 3/3/2009 - 3/6/2009
Lou Kondic New Jersey Institute of Technology 3/22/2009 - 3/26/2009
Ronnie Kosloff Hebrew University 3/1/2009 - 3/6/2009
Karl Kunisch Karl-Franzens-Universität Graz 2/28/2009 - 3/5/2009
Claude Le Bris CERMICS 9/11/2008 - 5/30/2009
Federico Lecumberry University of the Republic 3/23/2009 - 3/26/2009
Chiun-Chang Lee National Taiwan University 8/26/2008 - 7/31/2009
Catalin Lefter University "Al. I. Cuza" of Iaşi 2/28/2009 - 3/9/2009
Stacey E. Levine Duquesne University 3/22/2009 - 3/31/2009
Rachel Levy Harvey Mudd College 3/22/2009 - 3/27/2009
Jichun Li University of Nevada 3/22/2009 - 3/26/2009
Xiaofan Li Illinois Institute of Technology 3/22/2009 - 3/26/2009
Yongfeng Li University of Minnesota 9/1/2008 - 8/31/2010
Daniel Lidar University of Southern California 3/1/2009 - 3/4/2009
Hai Lin University of Colorado 3/1/2009 - 5/30/2009
Tai-Chia Lin National Taiwan University 8/23/2008 - 7/31/2009
Chun Liu University of Minnesota 9/1/2008 - 8/31/2010
Hsiang-Wei Lu Harvey Mudd College 3/22/2009 - 3/26/2009
Mitchell Luskin University of Minnesota 9/1/2008 - 6/30/2009
Yvon Maday Université de Paris VI (Pierre et Marie Curie) 3/2/2009 - 3/6/2009
Riccardo March Consiglio Nazionale delle Ricerche (CNR) 3/21/2009 - 3/26/2009
Vasileios Maroulas University of Minnesota 9/1/2008 - 8/31/2010
Craig C. Martens University of California, Irvine 3/3/2009 - 3/7/2009
Kevin Mcilhany U.S. Naval Academy 3/15/2009 - 3/19/2009
Kevin W. Mclaughlin University of Wisconsin - River Falls 1/6/2009 - 6/30/2009
David A. Micha University of Florida 3/2/2009 - 3/7/2009
Mario Micheli University of California, Los Angeles 3/22/2009 - 3/26/2009
Michael J. Miksis Northwestern University 3/22/2009 - 3/26/2009
William H. Miller University of California, Berkeley 3/1/2009 - 3/4/2009
Simon Peter Morgan Los Alamos National Laboratory 3/22/2009 - 3/28/2009
Abdul Rehaman Moughal Shahi Université de Genève 2/2/2009 - 6/30/2009
Shaul Mukamel University of California, Irvine 3/1/2009 - 3/5/2009
Andreas Münch University of Nottingham 3/22/2009 - 3/26/2009
Nebo Murisic University of California, Los Angeles 3/22/2009 - 3/25/2009
Ali Nadim Claremont Graduate University 3/22/2009 - 3/26/2009
Kazuyuki Nakagami Tohoku University 2/28/2009 - 3/7/2009
Barbara Niethammer University of Oxford 3/21/2009 - 3/26/2009
James Hilton Nolen Duke University 3/22/2009 - 3/25/2009
Amy Novick-Cohen Technion-Israel Institute of Technology 3/22/2009 - 3/27/2009
Adam Oberman Simon Fraser University 3/22/2009 - 3/26/2009
Yukiyoshi Ohtsuki Tohoku University 2/28/2009 - 3/7/2009
Stanley J. Osher University of California, Los Angeles 3/24/2009 - 3/26/2009
Miguel Sebastian Pauletti University of Maryland 3/22/2009 - 3/26/2009
Ellen Peterson North Carolina State University 3/22/2009 - 3/25/2009
Oleg Prezhdo University of Washington 3/3/2009 - 3/6/2009
Jean-Pierre Puel Université Versailles/Saint Quentin-en-Yvelines 3/1/2009 - 3/8/2009
Mary Pugh University of Toronto 3/22/2009 - 3/25/2009
Herschel A. Rabitz Princeton University 2/28/2009 - 3/5/2009
Viswanath Ramakrishna University of Texas at Dallas 3/1/2009 - 3/6/2009
Nancy Rodriguez University of California, Los Angeles 3/23/2009 - 3/27/2009
Darragh Patrick Rooney University of Michigan 3/1/2009 - 3/6/2009
Pierre Rouchon École Nationale Supérieure des Mines de Paris 3/1/2009 - 3/6/2009
William Rozzi Eastman Kodak Company 3/23/2009 - 3/26/2009
Martin Rumpf Rheinische Friedrich-Wilhelms-Universität Bonn 3/21/2009 - 3/25/2009
Julien Salomon Université de Paris IX (Paris-Dauphine) 2/27/2009 - 3/6/2009
Fadil Santosa University of Minnesota 7/1/2008 - 6/30/2010
Guillermo R. Sapiro University of Minnesota 3/22/2009 - 3/26/2009
Alain Sarlette Université de Liège 2/28/2009 - 3/7/2009
Andreas Savin Université de Paris VI (Pierre et Marie Curie) 3/22/2009 - 4/2/2009
Arnd Scheel University of Minnesota 9/1/2008 - 6/30/2009
Sonia Schirmer University of Cambridge 2/28/2009 - 3/7/2009
L. Ridgway Scott University of Chicago 9/1/2008 - 6/30/2009
Tsvetanka Sendova University of Minnesota 9/1/2008 - 8/31/2010
Yuk Sham University of Minnesota 9/1/2008 - 6/30/2009
Michael Shearer North Carolina State University 3/22/2009 - 3/25/2009
Michael J. Shelley New York University 3/23/2009 - 3/26/2009
Amy Shen University of Washington 3/22/2009 - 3/26/2009
Heinz Siedentop Ludwig-Maximilians-Universität München 1/14/2009 - 4/21/2009
Robert D. Skeel Purdue University 3/29/2009 - 6/27/2009
Linda B. Smolka Bucknell University 3/22/2009 - 3/26/2009
Vladimir A. Sobolev Samara State University 2/16/2009 - 3/16/2009
James Springham University of Leeds 3/22/2009 - 3/27/2009
Andrew M. Stein University of Minnesota 9/1/2007 - 5/1/2009
Rob Sturman University of Leeds 3/22/2009 - 3/27/2009
Huan Sun Pennsylvania State University 2/5/2009 - 5/31/2009
Pengtao Sun University of Nevada 3/22/2009 - 3/26/2009
Ganesh Sundaramoorthi University of California, Los Angeles 3/24/2009 - 3/27/2009
Li-yeng Sung Louisiana State University 3/22/2009 - 3/26/2009
Peter Takac Universität Rostock 2/1/2009 - 3/31/2009
David J. Tannor Weizmann Institute of Science 3/1/2009 - 3/6/2009
Tzyh-Jong Tarn Washington University 3/1/2009 - 3/6/2009
Joseph M. Teran University of California, Los Angeles 3/22/2009 - 3/25/2009
Minassie Tewoldebrhan University of Minnesota 3/23/2009 - 3/26/2009
Burt S. Tilley Franklin W. Olin College of Engineering 3/19/2009 - 3/26/2009
Chad Michael Topaz Macalester College 3/23/2009 - 3/26/2009
Michael Trick Carnegie Mellon University 3/4/2009 - 3/5/2009
Donald G. Truhlar University of Minnesota 9/1/2008 - 6/30/2009
Gabriel Turinici Université de Paris IX (Paris-Dauphine) 2/28/2009 - 3/6/2009
Erkan Tüzel University of Minnesota 9/1/2007 - 8/7/2009
David Thomas Uminsky Boston University 3/22/2009 - 3/26/2009
Yves van Gennip Simon Fraser University 3/22/2009 - 3/26/2009
Rui Vilela Mendes Instituto Superior Tecnico 2/28/2009 - 3/7/2009
Gregory John von Winckel Karl-Franzens-Universität Graz 3/2/2009 - 3/6/2009
Shawn W. Walker New York University 3/22/2009 - 3/26/2009
Zhian Wang University of Minnesota 9/1/2007 - 8/31/2009
Guowei Wei Michigan State University 3/22/2009 - 3/26/2009
Stephen Wiggins University of Bristol 1/10/2009 - 6/30/2009
JF Williams Simon Fraser University 3/22/2009 - 3/26/2009
Thomas Peter Witelski Duke University 3/22/2009 - 3/25/2009
Wei Xiong University of Minnesota 9/1/2008 - 8/31/2010
Xiang Xu Pennsylvania State University 1/26/2009 - 6/1/2009
YiJing Yan Hong Kong University of Science and Technology 3/1/2009 - 3/6/2009
Ke Yang University of Minnesota 3/2/2009 - 3/6/2009
Anthony J. Yezzi Georgia Institute of Technology 3/22/2009 - 3/29/2009
Nung Kwan Yip Purdue University 3/22/2009 - 3/28/2009
Linghai Zhang Lehigh University 3/1/2009 - 3/7/2009
Wendy W. Zhang University of Chicago 3/22/2009 - 3/24/2009
Xiao Zheng Hong Kong University of Science and Technology 3/1/2009 - 3/7/2009
Weigang Zhong University of Minnesota 9/1/2008 - 8/31/2010
Yu Zhuang Texas Tech University 3/2/2009 - 3/6/2009
Yu Zhuang Texas Tech University 3/22/2009 - 3/27/2009
Enrique Zuazua Basque Center for Applied Mathematics 3/1/2009 - 3/7/2009
Legend: Postdoc or Industrial Postdoc Long-term Visitor

IMA Affiliates:
Arizona State University, Boeing, Corning Incorporated, ExxonMobil, Ford, General Motors, Georgia Institute of Technology, Honeywell, IBM, Indiana University, Iowa State University, Kent State University, Korea Advanced Institute of Science and Technology (KAIST), Lawrence Livermore National Laboratory, Lockheed Martin, Los Alamos National Laboratory, Medtronic, Michigan State University, Michigan Technological University, Microsoft Research, Mississippi State University, Motorola, Northern Illinois University, Ohio State University, Pennsylvania State University, Purdue University, Rice University, Rutgers University, Sandia National Laboratories, Schlumberger Cambridge Research Laboratories, Schlumberger-Doll, Seoul National University, Siemens, Telcordia, Texas A & M University, University of Central Florida, University of Chicago, University of Cincinnati, University of Delaware, University of Houston, University of Illinois at Urbana-Champaign, University of Iowa, University of Kentucky, University of Maryland, University of Michigan, University of Minnesota, University of Notre Dame, University of Pittsburgh, University of Tennessee, University of Wisconsin, University of Wyoming, US Air Force Research Laboratory, Wayne State University, Worcester Polytechnic Institute